Brandon buys a radio for 43.99 in a state where sales tax is 7%.What is the total brandon pays for the radio
Mr. Andrews has a classroom of 45 students. He wants to divide them equally into 5 teams for a group project.
How many students will be on each team?
A) 7
B) 8
C) 9
D) 10 what the answer
please help me with this, image attached.
Answer:
i believe it is c)82 but i may be wrong
Step-by-step explanation:
Write an expression to represent: Nine minus the quotient of two and a number x.
Answer:
9 - 2/x
Step-by-step explanation:
Please check if u can help!!
Answer: D
Step-by-step explanation:
David - f(x) Ronald - g(x)
f(x) = [tex]\sqrt[3]{x-1}[/tex]
f(2) = [tex]\sqrt[3]{2-1}[/tex] = 1.00 1.26
f(4) = [tex]\sqrt[3]{4-1}[/tex] = 1.44 1.59
f(6) = [tex]\sqrt[3]{6-1}[/tex] = 1.71 1.82
f(10) = [tex]\sqrt[3]{10-1}[/tex] = 2.08 2.15
The side length for Ronald's box is greater than David's.
***********************************************************************
Answer: (0, 4)
Step-by-step explanation:
f(x) is an absolute value graph with a vertex at (0, 3).
f(x) is increasing from 0 to infinity ⇒ (0, ∞)g(x) is a parabola reflected across the x-axis with a vertex at (4, 12).
g(x) is increasing from negative infinity to 4 ⇒ (-∞, 4)Together: f(x) and g(x) are both increasing from 0 to 4 ⇒ (0, 4)
**********************************************************************
0 o---------------------o 4
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years.
The equation: P = 0.007 y 2 − 0.01 y + 122
gives a person's blood pressure, P , at age y years.
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 44 years.
B.) If a person's systolic pressure is 133.36 mm Hg, what is their age (rounded to the nearest whole year)?
Answer:
(A)The systolic pressure of a person of age 44 is 135.1 mm Hg
(B) If a person's systolic pressure is 133.36 mm Hg, their age is 41 years.
Step-by-step explanation:
Given : P = 0.007 y² - 0.01 y +122
where P is systolic pressure and y is age of a person
(A) Here age of the person, y =44
So, P =0.007 (44²) -0.01 (44) +122 = 13.552 -0.44 +122 = 135.112 =135.1 mm
∴ The systolic pressure of a person of age 44 is 135.1 mm Hg
(B) Here P = 133.36 mm Hg
So,
133.36 = 0.007 y² - 0.01 y +122
=>0.007 y² -0.01 y -11.36 =0
=> 7 y² -10 y -11360 =0
Solving the above quadratic equation using quadratic formula, we have
[tex]y = \frac{5+\sqrt{79545} }{7}[/tex]
or [tex]y = \frac{5-\sqrt{79545} }{7}[/tex]
y = 41 or y = -39.57
Since age cannot be negative, y= 41
∴ If a person's systolic pressure is 133.36 mm Hg, their age is 41 years.
The systolic pressure of a 44-year-old person is approximately 132.8 mm Hg, and a person with a systolic pressure of 133.36 mm Hg is roughly 46 years old.
Explanation:To answer this question, we will be using the given equation P = 0.007y^2 - 0.01y + 122, where P represents a person's systolic blood pressure and y represents their age.
A) To find the systolic pressure for a person aged 44 years, we substitute y=44 into the equation. This gives us P = 0.007 * (44)^2 - 0.01 * 44 + 122 = 132.8 mm Hg.
B) To find the age of a person with a systolic pressure of 133.36 mm Hg, we set P=133.36 and solve the equation for y. This can be done using methods such as factoring, completing the square, or using the quadratic formula. Upon solving, we find y roughly equals 46, so the person is approximately 46 years old when rounded to the nearest whole year.
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The graph shows the function f(x) = |x – h| + k. What is the value of h?
h = –3.5
h = –1.5
h = 1.5
h = 3.5
Answer:
h = –1.5
Step-by-step explanation:
we know that
In the function
[tex]f\left(x\right)=\left|x-h\right|+k[/tex]
The point (h,k) is the vertex of the function
where
h is the x-coordinate of the vertex
k is the y-coordinate of the vertex
In this problem the vertex is the point (-1.5,-3.5)
therefore
h=-1.5
the function is
[tex]f\left(x\right)=\left|x+1.5\right|-3.5[/tex]
see the graph in the attached figure
Hector spent $25.75 for 2 DVDs that cost the same amount. The sales tax on his purchase was $3.15. Hector also used a coupon for $1.00 off his purchase. How much did each DVD cost?
Answer:
The cost of each DVD is $11.8 .
Step-by-step explanation:
Let us assume that the cost of one DVD be x.
As given
Hector spent $25.75 for 2 DVDs that cost the same amount.
The sales tax on his purchase was $3.15.
Hector also used a coupon for $1.00 off his purchase.
Than the equation
Total Hector Spents for two DVDs = 2 × cost of one DVD + Sales tax + Coupon cost .
Putting the value
25.75 = 2x + 3.15 - 1.00
25.75 = 2x +2.15
25.75 - 2.15 = 2x
23.6 = 2x
[tex]x = \frac{23.6}{2}[/tex]
x = $11.8
Therefore the cost of each DVD is $11.8 .
Identify the perimeter and area of an equilateral triangle with height 12√2cm. Give your answer in simplest radical form. PLEASE HELP ASAP!!
Answer: (D) P=24√6, A=96√3
Step-by-step explanation:
Consider ΔABC where D is the midpoint of BC. Since ABC is an equilateral triangle, then segment AD is a perpendicular bisector with length of 12√2. This creates ΔADC which is a 30°-60°-90° triangle.
Now you can use the rules for this special triangle to find the length of the hypotenuse.
30° ⇄ side length "a" base - DC on ΔADC
60° ⇄ side length "a√3" height - AD on ΔADC
90° ⇄ side length "2a" hypotenuse - AC on ΔADC
Step 1: solve for "a"
[tex]AD: a\sqrt3=12\sqrt{12}[/tex]
[tex]\dfrac{a\sqrt3}{\sqrt3}=\dfrac{12\sqrt2}{\sqrt3}[/tex]
[tex]a=\dfrac{12\sqrt2}{\sqrt3}\bigg(\dfrac{\sqrt{3}}{\sqrt{3}}\bigg)[/tex]
[tex]= \dfrac{12\sqrt6}{3}[/tex]
[tex]=4\sqrt6[/tex]
Step 2: solve for "2a"
[tex]AC: 2a =2(4\sqrt{6})[/tex]
[tex]=8\sqrt{6}[/tex]
Step 3: find the perimeter
The side length is equivalent for all 3 sides so
P = 3(AC)
[tex]=3(8\sqrt{6})[/tex]
[tex]=24\sqrt{6}[/tex]
Step 4: find the area
[tex]A=\dfrac{1}{2}b \cdot h[/tex]
[tex]=\dfrac{1}{2}(8\sqrt6)(12\sqrt2)[/tex]
[tex]=(48\sqrt{12})[/tex]
[tex]=(96\sqrt3)[/tex]
A baseball team has played 9 games so far this season. The team won 7 games. What fraction of its games has the team won?
The baseball team has won 7 out of 9 games this season, which as a fraction is represented as 7/9.
Explanation:In order to find out the fraction of games the baseball team has won, we divide the number of games won by the total number of games played. In this case, the team has won 7 games out of 9 games played. Therefore, as a fraction, this is written as 7/9. This means that the team has won 7 out of every 9 games they've played so far this season.
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The baseball team has won 7 out of 9 games, so the fraction of games won is 7/9.
To calculate the fraction of games a baseball team has won, we divide the number of games won by the total number of games played. In this case, the team has won 7 games out of a total of 9 games played this season. To express this as a fraction, we write 7 as the numerator (the top number) and 9 as the denominator (the bottom number).
Therefore, the fraction of games the baseball team has won is 7/9.
Find the square root of these numbers to the nearest tenth.
72 =
32 =
481 =
Adriana made 30 pet collars to bring to the pet fair. She wants to display 3 pet collars on each hook. How many hooks will Adriana need to display all 30 pet collars
Answer:
10 hooks!
Step-by-step explanation:
if Adriana has 30 and wants to display 3 on each hook you would have to divide 30 by 3.
MATH HELP PLEASE!!
find the area of the shaded region.
use the formula A= pi r^2 to find the area of the circle.
a. 8pi x + 24pi
b. 8pi x - 24pi
c. x^2 + 8pi x + 24pi
d. x^2 +8pi x - 24pi
Without additional context or a visual, it's impossible to determine the correct answer for the area of the shaded region using the provided options and the circle area formula A = πr². More information about the figure is needed.
Explanation:The question asks to find the area of the shaded region using the area formula for a circle, which is A = πr².
However, without additional context or a diagram, it is impossible to provide a definitive answer to this question. Normally, to find the area of a shaded region involving a circle, one might calculate the area of the circle and then subtract the area of any unshaded parts that are inside the circle. However, the given answer options (a through d) suggest that the shaded region might involve an algebraic expression in terms of x. Based on typical problems, we might be dealing with a composite shape where x represents the dimension of another shape such as a square or rectangle. To find the correct answer, we would need to see the figure in question or have more information provided in the problem statement.
The area of the composite figure, which includes both the rectangle and the semicircle, is approximately [tex]\( 18.28 \)[/tex] square inches when calculated numerically The correct option is (b) is [tex]\( (8\pi + 12) \text{ in}^2 \)[/tex].
The provided image appears to show a composite figure consisting of a semicircle on top of a rectangle. To find the area of the composite figure, we need to calculate the area of the rectangle and the area of the semicircle separately, then add them together.
The formula to calculate the area of a rectangle is [tex]\( A = \text{length} \times \text{width} \)[/tex].
Given that the width of the rectangle (which is the same as the diameter of the semicircle) is 4 inches and the height (length) of the rectangle is 3 inches, the area of the rectangle is:
[tex]\[ A_{\text{rectangle}} = 4 \text{ in} \times 3 \text{ in} = 12 \text{ in}^2 \][/tex]
The formula to calculate the area of a circle is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius. Since we have a semicircle, we will take half of the area of a full circle. The diameter of the semicircle is 4 inches, so the radius [tex]\( r \)[/tex] is 2 inches.
The area of the semicircle is then:
[tex]\[ A_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2 \text{ in})^2 = 2 \pi \text{ in}^2 \][/tex]
Now, we'll add the areas of the rectangle and the semicircle to find the total area of the composite figure:
[tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 12 \text{ in}^2 + 2 \pi \text{ in}^2 \][/tex]
Let's calculate the total area.
The area of the composite figure, which includes both the rectangle and the semicircle, is approximately [tex]\( 18.28 \)[/tex] square inches when calculated numerically.
However, if we express the area in terms of [tex]\(\pi\)[/tex], the exact area is given by the formula:
[tex]\[ A_{\text{total}} = (8\pi + 12) \text{ in}^2 \][/tex]
Therefore, the correct answer is b. [tex]\( (8\pi + 12) \text{ in}^2 \)[/tex].
complete question given below:
What is the area of the composite figure?
(8pi+ 6) in2
(8pi+ 12) in2
(8pi+ 18) in 2
(8pi+ 24) in.2
expression to approximate log a of x for all positive numbers a, b, and x, where a is not equal to 1 and b is not equal to one
Question:
Approximate log base b of x, log_b(x).
Of course x can't be negative, and b > 1.
Answer:
f(x) = (-1/x + 1) / (-1/b + 1)
Step-by-step explanation:
log(1) is zero for any base.
log is strictly increasing.
log_b(b) = 1
As x descends to zero, log(x) diverges to -infinity
Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.
Find a such that f(b) = 1
1 = f(b) = (-1/b + 1)/a
a = (-1/b + 1)
Substitute for a:
f(x) = (-1/x + 1) / (-1/b + 1)
f(1) = 0
f(b) = (-1/b + 1) / (-1/b + 1) = 1
At a local fitness center, members pay an $8 membership fee and $4 for each aerobics class. Nonmembers pay $6 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Let X be the number of classes:
You need to multiply the cost per class by the number of classes.
For members you also need to add in the membership fee.
Members pay a total of 8 +4x
Non members pay a total of 6x
Set them to equal to solve for x, which is the number of classes taken:
8 + 4x = 6x
Subtract 4x from both sides:
8 = 2x
Divide both sides by 2:
x = 8/2 = 4
The answer is 4 classes.
A school replaced 20% of its computers with new ones what is the total number of computers in the school if 55 computers were replaced
Answer:
There were 275 computers
Step-by-step explanation:
Computers replaced = total computers * percent replaced
What do we know?
The percent replaced is 20 = .2
55 computers were replaced.
Substitute this in
55 = total computers * .2
Divide each side by .2
55/.2 = total computers *.2 /.2
275 = total computers
There were 275 computers
To find the total number of computers in the school, you set up the equation 0.20 * x = 55, where x is the total number of computers. Solving for x gives us x = 275, meaning there are 275 computers in the school.
The question is asking us to find the total number of computers in the school knowing that 20% of them were replaced and knowing that 55 computers were replaced. To find the total number of computers, we need to understand that the 55 computers represent the 20% that were replaced. So, we set up a proportion where 20% (0.20) of the total number of computers (which we will call x) equals to 55. The equation will look like this: 0.20 * x = 55.
We divide both sides of the equation by 0.20 to solve for x:
x = 55 / 0.20
x = 275
Thus, the total number of computers in the school is 275.
Help me with these math questions.. WITH SCREENIES
Answer: 3
Step-by-step explanation:
log₇343 = x
343 = 7ˣ
7³ = 7ˣ
3 = x
******************************************
Answer: 1950
Step-by-step explanation:
s = r θ
325π = r * 30 * [tex]\frac{\pi}{180}[/tex]
325 = r * [tex]\frac{\pi}{6}[/tex]
6(325) = r
1950 = r
******************************************
domain: x is All Real Numbers --> (-∞, ∞)
range: y > 0 --> (0, ∞)
y-intercept: when x = 0, y = e² --> e²
horizontal asymptote: since y ≠ 0, then H.A. is --> y = 0
Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).
y + 1 = -2(x – 5)
y – 1 = -2(x – 5)
y – 5 = -2(x + 1)
y -5 = -2(x – 1)
Answer:
[tex]y+1=-2(x-5)[/tex]
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and the slope.
We will substitute [tex]m=-2[/tex] and [tex]x_1=5\\y_1=-1[/tex].
[tex]y-(-1)=-2 (x-5)[/tex]
[tex]y+1=-2(x-5)[/tex]
This is the equation of the line with slope -2 that passes through (5,-1).
please help me with.
image attached.
m<1 is 90 degrees
m<2 is 121 degrees
m<3 is 42 degrees
m<4 is 42 degrees
m<5 is 35 degrees
m<6 is 90 degrees
m<7 is 48 degrees
m<8 is 35 degrees
m<9 is 35 degrees
6. The median-median line for a dataset is y=1.133x+0.489
The least-squares regression line for the same dataset is y=1.068x+0.731. Which regression equation better predicts the y-value for the point (50, 60)
A. The median-median line regression line is a better prediction.
B. The least squares regression line is a better prediction.
C. The models predict the same value
D. The models predict different values that are equally inaccurate
(1 point)
Answer: The answer is B...........
Answer:
The correct option is A. The median-median line regression line is a better prediction.
Step-by-step explanation:
The given median-median line for a dataset is
[tex]y=1.133x+0.489[/tex]
The least-squares regression line for the same dataset is
[tex]y=1.068x+0.731[/tex]
The given point is (50,60).
Substitute x=50 in each given equation.
[tex]y=1.133(50)+0.489=57.139[/tex]
[tex]y=1.068(50)+0.731=54.131[/tex]
Since the value of median-median line at x=50 is near to 60 than the value of least-squares regression at x=50.
The median-median line regression line is a better prediction. Therefore the correct option is A.
Which equation represents a line that has a slope of 4 and passes through the point (3,-8)?
Answer:
The equation of this line would be y + 8 = 4(x - 3)
Step-by-step explanation:
In order to get this we can start with the base form of point-slope.
y - y1 = m(x - x1)
Now that we've got this, we can plug in the slope for m. We can also plug in the point for (x1, y1).
y + 8 = 4(x - 3)
The sum of two numbers is 37
and the difference is 13
. What are the numbers?
Answer:
25, 12
Step-by-step explanation:
let x represent one number and y represent the other number
x+y=37 (sum is addition)
x-y=13 (difference is subtraction)
Im solving using the substitution method
x-y=13 add y to both sides to get x by itself
x=13+y
13+y+y=37 substitute x for the solution above in the other equation and simplify
2y=24
y=12
plug in y into one of the equations
x+12=37 subtract 12 from both sides
x=25
Use the graph of f(x) = |x(x2 − 1)| to find how many numbers in the interval [0.5, 0.75] satisfy the conclusion of the Mean Value Theorem.
Answer:
1 time
Step-by-step explanation:
f(x) = |x(x^2 − 1)|
The mean value theorem states
f'(c) = f(b) -f(a)
-------------
b-a
b = .75
a = .5
f(b) = abs(.75 * (.75^2 -1)) = abs (.75*(-.4375))=abs(-.328125)
= .328125
f(a) = abs(.5 * (.5^2 -1)) = abs(.5*(-.75))=abs(-.375) = .375
.328125- .375
f'(c) = -------------------------------------------------
.75-.5
f'(c) = -.1875
A pair of shoes costs $29.99 and the state sales tax is 5%. Use the formula C = p + rp to find the total cost of the shoes, where C is the total cost, p is the price, and r is the sales tax rate.
I've been struggling with this. I need help asap.
(Anyone that's good in math.)
The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years.
Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.
Answer:
y = 3500(3/7 ) ^ 1/3
y = 239.23
Step-by-step explanation:
For exponential decay
y =a b^x
a = 3500
b<1
We can use the point (3, 1500)
1500 = 3500 * b^3
Divide each by 3500
1500/3500 = 3500/3500 b^3
15/35 = b^3
3/7 = b^3
Take the cube root of each side
(3/7) ^ 1/3 = b^3 ^ 1/3
b = (3/7 ) ^ 1/3
The function is
y = 3500 (3/7) ^ 1/3 x
We want to find y when x=9.5
y = 3500 (3/7) ^ (9.5 /3)
y = 3500 ( 3/7) ^ 3. 166666666
y = 3500 (.06835)
y = 239.23
Lets check a point and see if we a close
(7,500)
y = 3500 (3/7)^ (1/3*7)
y = 3500 (3/7) ^ (7/3)
y = 484.68
That is pretty close. We do not know the exact value since we are reading from a graph.
A. y=4x-1 B. y=2x+7
C. y=3x-3 D. y=3x+3
The identified equations are linear as they conform to the standard linear format y = mx + b. They encompass scenarios like flu cases over years and predicted total hours for given square footage, all exhibiting linear relationships. Substituting particular x-values verifies solutions through identities.
Identifying Linear Equations
From the information provided, the task is to identify which equations are linear. A linear equation will generally have a format of y = mx + b, where m represents the slope and b represents the y-intercept. According to Practice Test 4 solutions, all three equations listed in option 1 (y = -3x, y = 0.2 +0.74x, y=-9.4 - 2x) are linear because they fit this model.
Additionally, the use of x and y in the context of independent and dependent variables is consistent with linear relationships. In the case of flu cases depending on the year, the year is independent and the number of cases is dependent. Similarly, relationships like the total number of hours required depending on the square footage, or the total payment based on the number of students, fit the linear model with an equation of the form y = mx + b.
Moreover, speaking of identities, when specific values of x are substituted in an equation resulting in an obvious equation such as 6 = 6, they confirm the solutions to the linear equation being correct.
A flagpole casts a 16-foot shadow at the same time a 4-foot pole casts a 5-foot shadow. How tall is the flagpole?
Set up a proportion:
The 4 foot pole casts a 5 foot shadow is written as 4/5
Let the height of the flagpole = x.
The flag pole casts a 16 foot shadow so it is written as X/16
Now set the two proportions equal to each other:
4/5 = X/16
Solve for X by cross multiplying:
5X = 64
Divide both sides by 5:
X = 64/5
X = 12.8
The flag pole is 12.8 feet tall.
Based on the information the tall of the flagpole is 12.8 feet tall .
Tall of the flagpoleSet up a proportion and let x = Height of the flagpole
4/5 =16/x
Solve x by cross multiplying
5x = 64
Divide both sides by 5x
x= 64/5
x=12.8 feet tall
Inconclusion the tall of the flagpole is 12.8 feet tall .
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The cost of 5 cans of dog food is $4.35.At the price,how much do 11 cans of dog foo cost.
Answer:
11 cans cost $9.57
Step-by-step explanation:
There are two ways of doing this, one being the longer and the other being the shorter.
The shorter one is simply multiplying the number by the new number over 5:
[tex]4.35 * \frac{11}{5}[/tex]
This works because this finds the amount the 5 has increased from 5 to 11 and muliplies the number by this.
[tex]4.35 * \frac{11}{5}[/tex] = 9.57
So 11 cans cost $9.57
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply. For any value of x, g(x) will always be greater than h(x). For any value of x, h(x) will always be greater than g(x). g(x) > h(x) for x = -1. g(x) < h(x) for x = 3. For positive values of x, g(x) > h(x). For negative values of x, g(x) > h(x).
ANSWER
g(x) > h(x) for x = -1 is TRUE
For positive values of x, g(x) > h(x) is TRUE
For negative values of x, g(x) > h(x) is also TRUE
EXPLANATION
The given functions are
[tex]g(x)={x}^{2}[/tex]
and
[tex]h(x)=-{x}^{2} [/tex]
If
[tex]x=0[/tex]
[tex]g(0)={0}^{2}=0[/tex]
[tex]h(0)=-({0})^{2}=0[/tex]
Based on this options A and B are FALSE.
When
[tex]x=-1[/tex]
[tex]g(-1)={( - 1)}^{2}=1[/tex]
[tex]h(-1)=-{(-1)}^{2}=-1[/tex]
[tex]g( - 1)>\:h(-1)[/tex]
for x=-1 is True.
When x=3,
[tex]g(3)={3}^{2}=9[/tex]
and
[tex]h(3)=-{3}^{2}=-9[/tex]
[tex]g(3)>\: h( 3)[/tex]
g(x) < h(x) for x = 3 is a FALSE statement.
For positive values of x, g(x) > h(x) is TRUE
See graph.
For negative values of x, g(x) > h(x) is also TRUE
See graph
The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are: h(x) will always be greater than g(x), g(x) < h(x) for x = 3, and for positive values of x, g(x) > h(x).
Explanation:The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are:
For any value of x, h(x) will always be greater than g(x).g(x) < h(x) for x = 3.For positive values of x, g(x) > h(x).These statements can be verified by plugging in values for x and comparing the outputs of the functions.
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25 PTS
The graph of the piecewise function is shown.
What is the range of f(x)?
{ f(x)| –∞ < f(x) < ∞}
{ f(x)| –∞ < f(x) ≤ 4}
{ f(x)| 4 < f(x) < ∞}
{ f(x)| 0 ≤ f(x) < ∞}
The range of the function f(x) is:
{ f(x) | –∞ < f(x) ≤ 4}
Step-by-step explanation:By looking at the graph of the function f(x) we see that in the interval :
(-∞,0]
The function f(x) takes a constant value as: f(x)=4
and after that i.e. for x≥0 , the function f(x) is decreasing continuously.
Hence, we could say that the function f(x) takes all the real values which are less than and equal to 4.
Hence, the range of the function is:
{ f(x)| –∞ < f(x) ≤ 4}