What transformations change the graph of (f)x to the graph of g(x)?
f(x) = x² ; g(x) = (x + 7)² + 9
Answers
The graph of g(x) is obtained by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
Further explanationTransformation of a graph: changing the shape and location of a graph.
We already know there are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).
The transformation that we will discuss is shifting horizontally or vertically.Translation (or shifting): moving a graph on an analytic plane without changing its shape.Vertical shift: moving a graph upwards or downwards without changing its shape.Horizontal shift: moving a graph to the left or right downwards without changing its shape.In general, given the graph of y = f(x) and k > 0, we obtain the graph of:
[tex]\boxed{ \ y = f(x) + k \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] upward k units.[tex]\boxed{ \ y = f(x) - k \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] downward k units.Furthermore in general, given the graph of y = f(x) and h > 0, we obtain the graph of:
[tex]\boxed{ \ y = f(x + h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the left h units.[tex]\boxed{ \ y = f(x - h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the right h units.,The combination of vertical and horizontal shifts is as follows:
[tex]\boxed{\boxed{ \ y = f(x \pm h) \pm k \ }}[/tex]
The plus or minus sign follows the direction of the shift, i.e., up-down or left-right
Given: [tex]\boxed{ \ f(x) = x^2 \ becomes \ g(x) = (x + 7)^2 + 9 \ }[/tex]
We set h = +7 and k = +9.
In the graph, additionally note the shift of points from (0, 0) to (-7, 9).
Conclusion
The graph of g(x) is drawn by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
Learn moreWhat is 270° converted to radians https://brainly.com/question/3161884A triangle is rotated 90° about the origin https://brainly.com/question/2992432What are the coordinates of the image of point B after the triangle ABC is rotated 270° about the origin? https://brainly.com/question/7437053Keywords: what transformations, change, the graph of f(x), to the graph of g(x), f(x) = x², g(x) = (x + 7)² + 9, translation, shifting, left, upward
The graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.
Further explanation:
The functions are given as follows:
[tex]\fbox{\begin\\\ \begin{aligned}f(x)&=x^{2}\\g(x)&=(x+7)^{2}+9\end{aligned}\\\end{minispace}}[/tex]
The objective is to determine the transformation or the way in which the graph of the function [tex]g(x)[/tex] is obtained from the graph of the function [tex]f(x)[/tex].
Concept used:
Shifting of graphs:
Shifting is a rigid translation because it does not change the size and shape of the curve. Shifting is used to move the curve vertically or horizontally without any change in shape and size of the curve.
The function [tex]y=f(x+a)[/tex] and [tex]y=f(x-a)[/tex] is a shift of the curve [tex]y=f(x)[/tex] horizontally towards negative and positive direction of [tex]x-[/tex]axis respectively.
The function [tex]y=f(x)+a[/tex] and [tex]y=f(x)-a[/tex] is a shift of the curve [tex]y=f(x)[/tex] vertically towards positive and negative direction of [tex]y-[/tex]axis respectively.
Step1: Draw the graph of the function [tex]f(x)=x^{2}[/tex].
Figure 1 (attached in the end) represents the graph of the function [tex]f(x)=x^{2}[/tex]. From figure 1 it is observed that the curve of the function [tex]f(x)=x^{2}[/tex] is a parabola with origin as the vertex and mounted upwards.
Step 2: Obtain the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] from the graph of the function [tex]f(x)=x2[/tex].
The function [tex]g'(x)=(x+7)^{2}[/tex] is of the form [tex]y=f(x+a)[/tex].
So, as per the concept of shifting of the graphs the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex]axis.
Figure 2 (attached in the end) represents the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].
In figure 2 the dotted line represents the curve of [tex]f(x)=x^{2}[/tex] and the bold line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex].
Step3: Obtain the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].
The function [tex]g(x)=(x+7)^{2}+9[/tex] is of the form [tex]y=f(x)+a[/tex].
So, as per the concept of shifting of graph the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] when each point on the curve of [tex]g'(x)=(x+7)^{2}[/tex] is shifted [tex]9[/tex] units towards upwards or the positive direction of [tex]y-[/tex]axis.
Figure 3 (attached in the end) represents the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex].
In figure 3 the dotted line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex] and the bold line represents the curve of [tex]g(x)=(x+7)^{2}+9[/tex].
From the above explanation it is concluded that the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.
Learn more:
1. A problem to determine the equation of line https://brainly.com/question/1646698
2. A problem on ray https://brainly.com/question/1251787
3. A problem to determine intercepts of a line https://brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Graphing
Keywords: Graph, curve, function, parabola, quadratic, f(x)=x2, g(x)=(x+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.
Related Questions
a(x+b)=c solve for x
Answers
x+b = c / A
x = c/A - b
Hope this helps!
The sum of two numbers is 10. if one number is subtracted from the other the result is -2. find two numbers
Answers
Form an equation to describe the situation
x+y=10
Then use the other information they gave you and form another equation
x-y=2
You can add the two equations together, and you see that the y variables cancel out(elimination)
2x=12
Solve for one variable and then plug it back into the original equation
x=6
6+y=10
y=4
The sum of the perimeters or two different squares is 32 centimeters , and the difference between there perimeters is 8 centimeters. if x represents the side length of the larger square and y represents the side length of the smaller square , Which of the following systems of equations could be used to find the dimensions of the squares?
A. x+y=32
x-y=8
B. 4x+4y=32
4x-4y=8
C. 2x+2y=32
2y-2x=8
D. 2x+2y=32
4x-2y=8
Answers
The correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.
Explanation:To find the dimensions of the squares, we can set up a system of equations. Let x represent the side length of the larger square and y represent the side length of the smaller square.
The sum of the perimeters is given as x + y = 32. The difference between the perimeters is given as x - y = 8.
So, the correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.
The correct system of equations to find the dimensions of the squares is x + y = 32 and x - y = 8. Solving this system using the method of elimination gives us the dimensions of the squares: 20 cm for the larger square and 12 cm for the smaller square.
Explanation:The correct system of equations to find the dimensions of the squares is:
x + y = 32
x - y = 8
To solve this system, we can use the method of elimination. Adding the two equations will eliminate the y terms, allowing us to solve for x.
Adding the equations:
x + y + x - y = 32 + 8
2x = 40
x = 20
Substituting the value of x back into one of the original equations, we can solve for y.
Using the equation x + y = 32:
20 + y = 32
y = 12
Therefore, the dimensions of the larger square are 20 cm, and the dimensions of the smaller square are 12 cm.
the total amount of degrees in the center is 360 degrees if all five vertex angles meeting the center are congrent what is the measure of a base angle of one of the triangles
A) 54 degrees
B) 72 degrees
C) 108 degrees
D) 144 degrees
Answers
Answer:
(B) 72°
Step-by-step explanation:
Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.
2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11
Answers
1) 2x + y + z = –7
2) x – 3y + 4z = –14
3) x – 2y – 3z = –11
elimination of x
2) - 3) -y + 7z = - 3
1) - 2.3) 5y +7z = 15
now we solve the simple system
-y + 7z = - 3 a)
5y +7z = 15 b)
elimination of y
5. a) + b) implies 42 z=12 and z= 2/7
-y +7 . 2/7= -3 implies y = 5
y=5, z =2/7, so 2x + 5 + 2/7 = –7 implies x= - 43/7
final solution
x= - 43/7, y=5 and z =2/7
proof
2.(- 43/7) + 5 + 2/7 = -7, (true)
How to put 0.258 0.4 0.52 1.25 0,04 from least to greatest?
Answers
Intersecting chords form a pair of congruent, vertical angles.
A. True
B. False
Answers
Answer:
True!
Step-by-step explanation:
The maximum speed of the Tupolev Tu -144 airliner is 694 m/s. What is this speed in kilometers per hour?
Answers
The speed is [tex]694m/s = \frac{694m}{1s} [/tex]
1 m = 0.001 km ⇒ 694 m = 694 * 0.001 km = 0.694 km
1 h = 60 min = 60 * 60 s = 3600 s
Therefore:
[tex] \frac{694m}{1s}= \frac{3600*0.694km}{3600s} = \frac{2498.4km}{1h} =2498.4km/h[/tex]
Answer: the correct answer would be 2498.4 km/h
*i got this question correct*
What is the surface area of a piece of pipe that is open at both ends, has a radius of 6 inches, and a height of 18 inches? (Use 3.14 for π.)
Answers
2π(6)(18)
you can imagine it like this:
imagine you take a sheet of paper and roll it into a tube
the lateral aera=circumference times height because if yo open the paper, the area is legnth times width, and when you roll it up, width turns into circumference
so
LA=h(circumference0
LA=h2pir
LA=18*2*pi*6
LA=216pi
pi=3.14 for this question
LA=678.24
SA=678.24 in²
Tomorrow, 567 people will want tickets to concert. only 417 tickets are available. how many people will be able to get tickets?
Answers
125 + .375=?
0.654 + 0.389 - 0.293=?
Answers
and for the second it's 0.75
0.654+0.389-0.293 equals0.75
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralf, and Peter weighs three times as much as Dominic. Together they weigh 720 pounds. How much does Dominic weigh?
Answers
1/2 x = 20 solve for x
Answers
2/2x=40
1x=40
x=40
the way i got that was i times .5 to 20 and got my answer because .5 is 1/2
Hopes this helps if you have more question just hmu and ask :)
280 divided by 30 what is it
Answers
The division yields to quotient is 9, and there is 10 as remainder
We have to divide 280 by 30.
So, the division performed as
30 | 280 | 9
270
-______
10
So, the quotient is 9, and there is 10 as remainder.
So, 280 divided by 30 is equal to 9.33 (rounded to two decimal places) or simply 9.
Learn more about Division here:
https://brainly.com/question/21416852
#SPJ6
The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3770. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x ...?
Answers
The hourly profit of an airline operating a plane can be calculated by subtracting the operating cost from the revenue earned from passengers.
Explanation:The hourly profit of an airline operating a plane can be expressed as the difference between the revenue earned from passengers and the operating cost of the plane.
The revenue earned from passengers can be calculated by multiplying the fare per passenger by the number of passengers. In this case, the fare is $100 per hour of flight, and the number of passengers is represented by x.
The operating cost of the plane is given as $3770 per hour.
Therefore, the hourly profit P can be expressed as:
P = (fare per passenger) * x - (operating cost of the plane)
Substituting the given values:
P = $100 * x - $3770
HELP ASAP!!!
The markup on appliances at Tom’s store is 50%. If the wholesale price of a dishwasher is $380, what price will Tom list when selling the dishwasher?
A. $570
B. $665
C. $760
D. $950
Answers
What is the area of a regular octagon with 12 as each side. Round to nearest hundredth.
Answers
How many times can 57 go into 413?
Answers
The only part of the United States explored by Russia was the:
A : Hudson River
B : Southwest and Mexico
C : Mississippi River
D : Northwest coastline
Answers
Answer:
d
Step-by-step explanation:
d
Evaluate 7 + (-3x2) for x = 0.
-2
0
4
7
Answers
7+(-3.0^2)
7+0
7
Answer:7+(-3.0^2)
7+0
7
Step-by-step explanation:
Write two (2) scenarios that describe two different real-world functions. Think of your own variables that are not included in the above list. As you did for the other functions, identify the independent and dependent variables and assign the letters x and y to represent each variable quantity. Then create a set of at least five ordered pairs in (x, y) form with values that make sense for your function.
Answers
2. Lexy has 456$ she gave it to four friends. Let M represent how much she gave each friend if she was left with 50$ What does X equal?
A prime number is always greater than 1 false or truth and why
Answers
hope this helps you
A prime number must be greater than 1 because by definition, a prime number has exactly two distinct positive divisors: 1 and the number itself. If a number is less than or equal to 1, it cannot be prime.
The statement that a prime number is always greater than 1 is indeed true. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. If a number is less than or equal to 1, it cannot be prime because the prime numbers must be greater than 1 to have at least two distinct positive divisors (1 and the number itself).
For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13. Each of these numbers is greater than 1 and cannot be divided evenly by any number other than 1 and itself. By contrast, the number 1 is not considered a prime because it has only one positive divisor, which is 1 itself. Since primes must have exactly two distinct divisors, 1 does not meet this criterion.
Given the function f(x) = x3 + 2x2 − 3x − 5, what is resulting function when f(x) is shifted to the right 1 unit?
Answers
f(x - 1) = (x - 1)^3 + 2(x - 1)^2 - 3(x - 1) - 5
= (x^3 - 3x^2 + 3x - 1) + 2(x^2 - 2x + 1) - 3(x - 1) - 5
= x^3 - 3x^2 + 2x^2 + 3x - 4x - 3x - 1 + 2 + 3 - 5
= x^3 - x^2 - 4x - 1
I hope this helps
The table shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days. It also shows the dollar amount taken in each day.
Hamburgers Hot Dogs Total
Day 1 200 150 $1,450
Day 2 200 250 $1,750
What is the cost of a hamburger and the cost of a hot dog?
Enter your answers in the boxes.
Hamburger: $
Hot dog: $
Answers
Based on the table shown above the cost of the hamburger is USD 5 and the cost of hot dog is USD 3
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, AB and CD , which of these conditions needs to be met to prove that AB is perpendicular to CD?
see attachment for choices
Answers
it is c)
[y4-y3/x4-x3][y2-y1/x2-x1]= -1
proof
two lines are perpendicular if the product of their slope equals -1
Answer:
[tex]\frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]
Step-by-step explanation:
We know that,
If two line segments are perpendicular then the product of their slope is equal to -1,
Also, the slope of a line segment having the end points [tex](x_n,y_n)[/tex] and [tex](x_m,y_m)[/tex] is,
[tex]m=\frac{y_m-y_n}{x_m-x_n}[/tex]
So, the slope of line segment AB having end points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is,
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]
Similarly, the slope of line segment CD having end points [tex]C(x_3,y_3)[/tex] and [tex](x_4,y_4)[/tex] is,
[tex]m_2=\frac{y_4-y_3}{x_4-x_3}[/tex]
Hence, by the above property of perpendicular line segments ,
If AB and CD are perpendicular then,
[tex]m_1\times m_2=-1[/tex]
[tex]\implies \frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]
Third option is correct.
Find the vertex of a function f(x)=-3x^2+9x-15 by completing the square
Answers
60 minutes is 20% of ? minute s
Answers
Which of the following represents the graph of f(x) = 2x + 2? i will give a medal if you help cooperatively
Answers
f(x) = 2^x + 2
To find which graph represents this function we should find at least 2 points. We take some value of x we want and calculate y for it. And do that at least 2 times (can be done 1 time but its likely that some graph match in some points)
for x = 0 we get
f(x) = 3
for x = 1
f(x) = 4
we can also note that f(x) cannot be less than 2 because 2^x is always greater than 0, and that as x increments f(x) increments. With all of this in mind answer is last graph.
Answer is graph D
Simplify.
1/4+4(1/2−3/4)^2
Answers
What is 830% written as a decimal?
8300
83
0.0083
8.3
8.3 i think