How can you use transformations to graph this function? y=3.7^{-x}+2 Explain your steps
Answers
Answer:
Steps are explained in the explanation part and graph is attached below.
Step-by-step explanation:
We have to graph the function [tex]y=3.7^{-x}+2[/tex] using the rule for transformation.
Let us suppose the parent function is [tex]y=3.7^x[/tex]. Below, is the graph of the parent function (fig 1)
When we add some constant 'c' in the function then the graph of the parent function shifts upward by 'c' units.
Hence, when we add 2 then the parent function will get shifted upward by 2 units. The graph of [tex]y=3.7^{x}+2[/tex] is attached below (fig 2)
Finally, x is replaced by -x hence the graph is reflected about y axis.
In figure 3 the graph of the given function is shown.
The graph of the function [tex]y = 3.7^{-x}+2[/tex] can be draw by using transformations. First shift the graph of [tex]y = 3.7^{x}[/tex] upwards by 2 units and then replace x by -x in the function [tex]y = 3.7^x+2[/tex] and graph of the function [tex]y = 3.7^x+2[/tex] is reflected about y-axis.
Given :
[tex]y = 3.7^{-x}+2[/tex]
To graph the above function using transformations following steps can be use:
Step 1 - Draw the graph of exponential function [tex]y = 3.7^{x}[/tex].
Step 2 - Now, shift the graph upwards in y axis by 2 units. The resulting graph is of function [tex]y = 3.7^x+2[/tex].
Step 3 - Now, replace x with -x in the function [tex]y = 3.7^x+2[/tex] and graph of the function [tex]y = 3.7^x+2[/tex] is reflected about y-axis. The resulting graph is of the function [tex]y = 3.7^{-x}+2[/tex] .
For more information, refer the link given below:
https://brainly.com/question/12465796
Related Questions
Find an equation for this inverse.
f(x) = 5x + 1
Please help! I have a test tomorrow & I have absolutely no idea on his to do this, thanks! :)
Answers
We have the function [tex]f(x)=5x+1[/tex]. Let's call our outputs "y", so we have [tex]y=5x+1[/tex]. To find the inverse, we're going to change the x and the y's position in the equation, so we have [tex]x=5y+1[/tex]. Then all we need to do is solve for y:
[tex]x=5y+1[/tex]
[tex]x-1=5y[/tex]
[tex]\frac{x}{5}-\frac{1}{5}=y[/tex]
[tex]f^{-1}(x)=y=\frac{x}{5}-\frac{1}{5}[/tex]
If so, then you can determine if a function has an inverse by passing the "horizontal line test."
This function does because it has a slope not equal to zero. Inverses of horizontal lines have vertical lines in them, which are not by definition functions.
So now, simply replace "f(x)" with "y", then switch the x and y, and solve for y:
y = 5x + 1
x = 5y + 1
-1 -1
5y = x - 1
÷5 ÷5
y = (x-1)/5
m ∠ A = 100 - x
m ∠ B = 80 + x
m ∠ C = 110 - 3x
m ∠ D = 75 + 2x
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 5
B) x = 7
C) x = 10
D) x = 15/2
Answers
100 - x = 110 - 3x
100 + 2x = 110
2x = 10
x = 5
m<A = 100 - x = 100 - 5 = 95
m<C = 110 - 3x = 110 - 3 * 5 = 110 - 15 = 95
Opposite angles A and C are congruent.
Now we need to check opposite angles B and D.
m<B = 80 + x = 80 - 5 = 75
m<D = 75 + 2x = 75 + 2 * 5 = 75 + 10 = 85
Opposite angles B and D are also congruent.
Answer: x = 5
Farmer jinzhou has 300 feet of fencing to enclose two identical rectangular pens that share a common fence. what are the dimensions of the pens that make their areas as large as possible? if x represents the length of the enclosure, what is the domain in the context of this situation?
Answers
Let the length of one of the three sides of the same length be x, then the length of one of the two sides of the same length is [tex] \frac{1}{2} (300-3x) [/tex].
The entire stucture is a stack of two identical rectangles which is also rectangular in shape.
The area of a rectangle is given by length times width. i.e.
[tex]Area= \frac{1}{2} x(300-3x)=150x- \frac{3}{2} x^2[/tex]
For maximum area, the derivative of the area with respect to x equals zero.
[tex] \frac{d}{dx} (Area)=150-3x=0 \\ \\ \Rightarrow3x=150 \\ \\ \Rightarrow x= \frac{150}{3} =50[/tex]
The length of one of the two sides of equal length is [tex]\frac{1}{2} (300-3(50))=\frac{1}{2}(150)=75[/tex]
Therefore, the dimensions of each pen that will make their areas as large as possible is 50 ft by 37.5 ft
For which value would the graph y= x^4 -25 be below the x axis?
Answers
Please help with these questions thank you.
Answers
1. 2 and 7 are equal
2. angle 1 = 68 degrees
3. 1st answer
Question 2(Multiple Choice Worth 15 points) (04.03 LC) Which of the following options results in a graph that shows exponential growth?
f(x) = 0.4(0.2)x
f(x) = 4(0.98)x
f(x) = 0.7(5)x
f(x) = 5(4)−x
Answers
The answer is: [C]: " f(x) = 0.7(5)ˣ " .
_________________________________________________________
Explanation:
_________________________________________________________
From all the answer choices given;
Answer choice: [C]: " f(x) = 0.7 (5)ˣ " ; is the answer choice with a "positive number"; {which is then multiplied by: [ a "positive whole number" or a "positive number greater than "1"; that is raised to a "positive variable"] .
________________________________________________
How I solved this: Further Explanation:
________________________________________________
A positive number multiplied by a {"number less than 1; raised to "x"] would result in increasingly lower values as "x" increases. Same with "raised to "negative x" {refer to "Answer choice [D]" }.
Answer:
The answer is: [C]: f(x) = 0.7(5)ˣ
Step-by-step explanation:
What is the value of the expression? (−3)3+6312
Answers
-9+6312
6303
The answer is 6303. Hope this helps!
Simplify 5 to the second power
Answers
James is writing a coordinate proof involving a parallelogram. Knowing that the opposite sides of a parallelogram are congruent, James places his parallelogram on the coordinate plane such that one vertex is at the origin and one side lies along the x-axis. What coordinates should he assign to the fourth vertex of the parallelogram? (2a, a) (2a, a2) (a2, 0) (2a, 2a)
Answers
is ur answer
hope this helps
Answer:-(2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
Explanation:-
Let ABCD be the vertices of the given parallelogram such that A=(0.,0) , B=(a,0) , C(x,y) and D=(a,a)
Construct the diagonals AC and BD of parallelogram ABCD .
We know that diagonals of a parallelogram bisect each other.
⇒ mid point of AC= mid point of BD...(1)
Mid point of BD[tex]=(\frac{a+a}{2},\frac{0+a}{2})=(\frac{2a}{2},\frac{a}{2})=(a,\frac{a}{2})[/tex]........(2)
Mid point of AC[tex]=(\frac{0+x}{2},\frac{0+y}{2})=(\frac{x}{2},\frac{y}{2})[/tex]......(3)
Substitute (2) and (3) in (1), we get
[tex](\frac{x}{2},\frac{y}{2})=(a,\frac{a}{2})\\\Rightarrow\frac{x}{2}=a;\frac{y}{2}=\frac{a}{2}[/tex]
[tex]\Rightarrow\ x=2a\ and\ y=a[/tex]
⇒C=(2a,a)
⇒ (2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
Explain how to determine if these two are the same function expressed in different ways
Answers
Answer:
Sample Answer:
When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.
Step-by-step explanation:
Answer:
When a linear function is expressed in different forms, its slope and y-intercept remain the same. The slope from the equation is -1, and the y-intercept from the equation is 3. The slope from the table is -1, and the y-intercept from the table is −3. These are not the same functions.
Step-by-step explanation:
Assume that a randomly selected subject is given a bone density test. those test scores are normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a given score is less than 1.66 and draw a sketch of the region.
Answers
μ = 0, the population mean
σ = 1, the population standard deviation
For the random variable x = 1.66, the z-score is
z = (1.66 - 0)/1 = 1.66
From standard tables,
P(x < 1.66) = 0.952
Answer:
0.952 or 952%
The area (probability) is shown in the figure.
If the following fraction is reduced, what will be the exponent on the q? -5p^5q^4/ 8p^2q^2
Answers
I did this question already. The answer is 2
If a triangle is an isosceles triangle, then it has two sides of equal length. If a triangle has two sides of equal length, then it has two angles of equal measure
Conclusion:
If a triangle is an isosceles triangle, then it has two angles of equal measure.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of syllogism.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
Answers
we know that
The Law of Syllogism says that if the following two statements are true:
(1) If p -------> then q .
(2) If q-------> then r .
Then we can derive a third true statement:
(3) If p--------> then r .
In this problem
(1) If a triangle is an isosceles triangle, then it has two sides of equal length
(2) If a triangle has two sides of equal length, then it has two angles of equal measure
Let
p-------> the statement " an isosceles triangle"
q--------> the statement " has two sides of equal length"
r---------> the statement "has two angles of equal measure"
Then (1) and (2) can be written
1) If p , then q .
2) If q , then r .
So, by the Law of Syllogism, we can deduce
3) If p , then r
or
If a triangle is an isosceles triangle, has two angles of equal measure
therefore
the answer is
The argument is valid by the law of syllogism.
Find the volume of the pyramid. Round your answer to the nearest hundredth.
A. 146.61
B. 154.87
C. 164.61
D. 186.61
Answers
What is the first term of the geometric sequence presented in the table below?
n 5 7
an 176 704
Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.
Answers
704 = a1 * r^6
dividing:-
r^2 = 706/174 = 4 so r = +/- 2
a1 = 176 / 2^4 = 176/16 = 11
So 11 is the first term
a family is canoeing (with the current). Their speed relative to the banks of the river averages 2.75mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Write and solve a system of equations to find the family’s paddling speed in still water.
Answers
Answer:
it's 2.125
Step-by-step explanation:
The required speed of family's paddling speed in still water is 2.125 mi/h.
Given that,
A family is canoeing (with the current). Their speed relative to the banks of the river averages 2.75mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relatives to the riverbank.
Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
Let the speed of the family on still water be x,
Speed of the current be y
According to the question,
upstream speed,
1.5 = x - y - - - - - (1)
Downstream speed,
2.75 = x + y - - - - - (1)
Solving equations 1 and 2 givens,
2x = 4.25
x = 2.125 mi / h
Thus, the required speed of the family paddling speed in still water is 2.125 mi/h.
Learn more about speed here:
https://brainly.com/question/7359669
#SPJ5
True or False:
The domain of the composite function (f◦g)(x) is the same as the domain of g(x).
Answers
The statement is false. The domain of the composite function (f◦g)(x) is not always the same as the domain of g(x). It includes only the values of x for which both g(x) and f(g(x)) are defined.
Explanation:The statement is False. The domain of the composite function (f◦g)(x) is not always the same as the domain of g(x). In a composite function (f◦g)(x), the domain includes only the values of x for which both g(x) and f(g(x)) are defined.
For example, if g(x) = sqrt(x) and f(x) = 1/x, the domain of g(x) would be all real numbers x ≥ 0, but the domain of the composite function (f◦g)(x) = 1/sqrt(x) would be x > 0, because 1/sqrt(x) isn't defined for x = 0.
Learn more about Composite Function here:https://brainly.com/question/36505829
Which ordered pair is a solution to this equation?
2x+6y=10
A (12, 2)
B (4, 1)
C (3, 1)
D (2, 1)
Answers
State 7m to 250cm as a ratio in its lowest terms
Answers
To go from meters to centimeters you multiply the number by 100.
7*100=700cm
Now you have 700cm/250cm. This needs simplified
I divided each number by 50 to get 14 and 5
14cm/5cm or 14cm:5cm
Final answer:
To express the ratio of 7 meters to 250 centimeters in its lowest terms, convert both to the same unit and simplify. 7 meters is 700 centimeters, leading to an initial ratio of 700:250, which simplifies to a final ratio of 14:5.
Explanation:
To state 7m to 250cm as a ratio in its lowest terms, we need to convert them to the same unit. One meter is equivalent to 100 centimeters, so 7 meters is the same as 700 centimeters.
Now we can write the ratio as 700 cm : 250 cm, which can be simplified by dividing both terms by 250 cm (the greatest common divisor of both numbers).
The simplified ratio is 700÷ 250 : 250÷ 250, which simplifies to 7 : 2.5. Since we want the ratio in its lowest terms with whole numbers, we can multiply both terms by 2 to eliminate the decimal, resulting in a final ratio of 14 : 5.
What is the solution set to the equation (2x−4)(4x−5)=0
Answers
Answer:
[tex]\left \{ 2,\frac{5}{4} \right \}[/tex]
Step-by-step explanation:
We know that for equation of type [tex](x-a)(x-b)=0[/tex], solutions are [tex]x=a\,,\,x=b[/tex] as both points x = a and x = b satisfy the equation (x-a)(x-b)=0
Given : equation (2x−4)(4x−5)=0
To find : Solution set of this equation .
Solution :
On dividing this equation by 2 and 4, we get
[tex]\left ( \frac{2x-4}{2} \right )\left ( \frac{4x-5}{4} \right )=0\\\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0[/tex]
On comparing equation [tex]\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0[/tex] with [tex]\left ( x-a \right )\left ( x-b \right )=0[/tex], we get [tex]a=2\,,\,b=\frac{5}{4}[/tex]
Therefore, solution set is [tex]\left \{ 2,\frac{5}{4} \right \}[/tex]
Final answer:
The solution set to the equation (2x−4)(4x−5) = 0 is {2, 5/4}.
Explanation:
The equation (2x−4)(4x−5) = 0 represents a quadratic equation. To solve this equation, we can set each factor equal to zero and solve for x. So we have:
2x - 4 = 0, which gives x = 2
4x - 5 = 0, which gives x = 5/4
Therefore, the solution set to the equation is {2, 5/4}.
What value of k makes the statement true? xky4(2x3 + 7x2y4) = 2x4y4 + 7x3y8 k =
Answers
The answer is "1".
Answer: Answer is 1
Step-by-step explanation:
edge
Plz halp. I just need #20, and please write out the equation so I know how to do it for future problems, thanks!
Answers
Hope this help!
Have a Great day mate !!
A recipe uses 3 cups of water, 2 cups of rice, and 1 cup of black beans. What is the ratio of cups of rice to cups of water?
Answers
Final answer:
The ratio of cups of rice to cups of water in the recipe is 2 to 3, which can also be written as 2/3.
Explanation:
The question asks us to find the ratio of cups of rice to cups of water. The recipe provided uses 2 cups of rice and 3 cups of water. To find this ratio, we simply compare the number of cups of rice to the number of cups of water and write it as a fraction or a division problem.
In this case, the ratio is:
2 cups of rice : 3 cups of water
Which we can also write as 2/3 or say that for every 2 cups of rice, there are 3 cups of water.
Please Help!
Which is true about the domain and range of a function in the form f(x) = m, where m is a real number greater than 0?
The only value that must be in both the domain and range is 0.
The only values that must be in both the domain and range are 0 and 1.
There are no values that are in the domain and the range.
There is an infinite number of values that are in both the domain and range.
Answers
Answer:
infinite number of values in domain and range
Step-by-step explanation:
need points for finals
For a function of the form f(x) = m, the domain is all real numbers and the range is the single real number m. Thus, there are no values that are in both the domain and the range.
Explanation:In a function of the form f(x) = m, where m is a real number greater than 0, the domain encompasses all real numbers since there are no restrictions on any values of x that would make the function undefined. Since the function gives the same result (m) regardless of what x is, f(x) remains constant. Thus, the range only contains one real number, which is m.
The correct option from the ones given, therefore, is: There are no values that are in the domain and the range. This is because the domain contains all real numbers, while the range contains only one number (m), and these sets do not overlap.
Learn more about Domain and Range here:https://brainly.com/question/36903938
#SPJ11
help please
Find the volume of a pyramid with a square base, where the perimeter of the base is 5.5 m and the height of the pyramid is 2.9 m. Round your answer to the nearest tenth of a cubic meter.
Answers
V= ⅓[ (5.5÷4)² × 2.6]
v= ⅓[ 4.92]
v = 1.6m³
In this particular arithmetic sequence, a7 = 50 and a15 = 114. What is the value of a21? Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.
Answers
Hope this helped, and if it did I'd appreciate if you marked me as brainliest as I need it to get to a higher rank. If you need any more help, feel free to add me and/or message me :)
An equation that contains only the operation of addition is called
Answers
__________________________________________
You board a Ferris wheel at ground level and travel to the very top, when it stops to allow more riders to get on.
How many degrees has the Ferris wheel rotated?
Answers
Answer:
answer is 180 degrees
Step-by-step explanation:
180 degrees has the Ferris wheel rotated
What is rotation?Rotation is the circular movement of an object around an axis of rotation.
Given:
There is ferries wheel when we board on ferris wheel it will be considered as 0 degree.
but when the ferris wheel stop to get more riders on at that time we are vey top.
So, we have covered half of the complete angle i.e., 180 degree
Hence, the ferris wheel cover 180 degrees.
Learn more about rotation here:
https://brainly.com/question/1571997
#SPJ2
MATH HELP PLEASE!!!!
Answers
1. any number times2 then subtracted by the same number can't = 0 , so it is Null Set
2. 2^2 = 4 +12 = 16, 8*2 = 16, answer is 2
a line segment has endpoints (4,7) and (1,11).what is the length of the segment
Answers
x1 for 4, y1 for 7, x2 for 1, y2 for 11
2. put them together. D= Square root (1-4)^2 + (11-7)^2
3. D= square root (-3)^2 +(4)^2
4. D= Square root 9+16
5. D= square root 25
6. D= -5