Question

Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function y = x² and show all stages. Be sure to identify at least three key points. Find the domain and the range of the function. f(x) = x² – 11 Which of the following transformations of y = x² need to be applied to graph f(x) = x² – 11? Select all that apply. A. Horizontal compression B. Vertical stretch C. Horizontal shift D. Horizontal stretch E. Reflection about the x-axis F. Reflection about the y-axis G. Vertical compression H. Vertical shift Fill in the missing coordinates of the points that lie on the graph of y = x² and the corresponding points that lie on the graph of f(x) = x² – 11. Points that lie on the graph of y = x² (Simplify your answers.) | Corresponding points that lie on the graph of f(x) = x² – 11 (Type ordered pairs. Simplify your answer.) (-2, ) (0, ) (2, ) The domain of f(x) is . (Type your answer in interval notation.) The range of f(x) is . (Type your answer in interval notation.)

          Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function y = x² and show all stages. Be sure to identify at least three key points. Find the domain and the range of the function.
f(x) = x² – 11
Which of the following transformations of y = x² need to be applied to graph f(x) = x² – 11? Select all that apply.
A. Horizontal compression
B. Vertical stretch
C. Horizontal shift
D. Horizontal stretch
E. Reflection about the x-axis
F. Reflection about the y-axis
G. Vertical compression
H. Vertical shift
Fill in the missing coordinates of the points that lie on the graph of y = x² and the corresponding points that lie on the graph of f(x) = x² – 11.
Points that lie on the graph of y = x² (Simplify your answers.) | Corresponding points that lie on the graph of f(x) = x² – 11 (Type ordered pairs. Simplify your answer.)
(-2, )
(0, )
(2, )
The domain of f(x) is .
(Type your answer in interval notation.)
The range of f(x) is .
(Type your answer in interval notation.)

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Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function y = x² and show all stages. Be sure to identify at least three key points. Find the domain and the range of the function.
f(x) = x² – 11
Which of the following transformations of y = x² need to be applied to graph f(x) = x² – 11? Select all that apply.
A. Horizontal compression
B. Vertical stretch
C. Horizontal shift
D. Horizontal stretch
E. Reflection about the x-axis
F. Reflection about the y-axis
G. Vertical compression
H. Vertical shift
Fill in the missing coordinates of the points that lie on the graph of y = x² and the corresponding points that lie on the graph of f(x) = x² – 11.
Points that lie on the graph of y = x² (Simplify your answers.) | Corresponding points that lie on the graph of f(x) = x² – 11 (Type ordered pairs. Simplify your answer.)
(-2, )
(0, )
(2, )
The domain of f(x) is .
(Type your answer in interval notation.)
The range of f(x) is .
(Type your answer in interval notation.)

Added by Ryan S.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Julie Silva

03/16/2022

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**Step 2: Find the corresponding points on the graph of \(y = x^2\) and \(f(x) = x^2 - 11\)** Show more…

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Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function y = x² and show all stages. Be sure to identify at least three key points. Find the domain and the range of the function. f(x) = x² – 11 Which of the following transformations of y = x² need to be applied to graph f(x) = x² – 11? Select all that apply. A. Horizontal compression B. Vertical stretch C. Horizontal shift D. Horizontal stretch E. Reflection about the x-axis F. Reflection about the y-axis G. Vertical compression H. Vertical shift Fill in the missing coordinates of the points that lie on the graph of y = x² and the corresponding points that lie on the graph of f(x) = x² – 11. Points that lie on the graph of y = x² (Simplify your answers.) | Corresponding points that lie on the graph of f(x) = x² – 11 (Type ordered pairs. Simplify your answer.) (-2, ) (0, ) (2, ) The domain of f(x) is . (Type your answer in interval notation.) The range of f(x) is . (Type your answer in interval notation.)

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Transcript

00:01 So the ultimate goal for this problem is to graph the function f of x equals x squared minus 11 by using transformations to the graph of y equals x square.

00:09 Well, notice that compared to our original function, our parent function, y equals x squared, all we're doing is we're taking the function and subtract the 11.

00:17 Well, that means that all of our values are going to get shifted down 11 units.

00:22 So in this particular case, we call this a vertical shift.

00:25 So h is going to be the only option here that you need to worry about checking our.

00:30 Off if we're going to have a vertical shift.

00:33 Now, the second part is we want to fill in the blinks.

00:36 So what we want to do first is we want to take negative 2 blank, and then we're going to transform it to our original function.

00:43 So first, we need to find what the value would be on the graph y equals x squared, and then by using our vertical shift, we can then apply it to the graph for x squared minus 11.

00:54 So first, let's substitute negative 2 for x.

00:57 So we have y equals negative 2 square.

00:59 Well, negative 2 squared is equal to 4.

01:02 So negative 2 .4 is on the graph of y equals x squared.

01:05 But remember, our graph is getting shifted down 11 units.

01:08 So essentially, we take 4 and subtract 11 by it, which is negative 7.

01:12 So we know negative 2, negative 7 will be on our graph.

01:16 Next worded pair we have is 0 and blank.

01:19 So we'll substitute it in.

01:20 Well, 0 squared is equal to 0.

01:22 And then again, we're going to subtract 11 from the y value, which means the ordered pair is 0, negative 11, is on our new graph...

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