Quiz about 1.4 Inverse of Quadratics Scholars

Question 1

What does it mean to find the inverse of a function?

Accepted Answer

the x's and y's are switched

Answer

the x's and y's are divided by 2

Answer

the x's and y's are made negative

Answer

the x's and y's are the same

Question 2

Identify the inverse function

$$y=\sqrt{\ x+5}-1$$

Accepted Answer

$$f^{-1}\left(x\right)=\left(x+1\right)^2-5$$

Answer

$$f^{-1}\left(x\right)=-\left(x-5\right)^2+1$$

Answer

$$f^{-1}\left(x\right)=\left(x-1\right)^2+5$$

Answer

$$f^{-1}\left(x\right)=\left(x+4\right)^2$$

Question 3

The inverse of the function f(x) is written as ...

Accepted Answer

f -1(x)

Answer

f 2(x)

Answer

f '(x)

Answer

f +(x)

Question 4

Restricting the domain is another way to say restricting the...

Accepted Answer

x-values

Answer

y-values

Answer

Odd numbers

Answer

Even numbers

Question 5

A function has an inverse function if...

Accepted Answer

It passes the Vertical Line Test and the Horizontal Line Test.

Answer

It fails the Horizontal Line Test

Answer

It passes only the Horizontal Line Test

Answer

It fails the Vertical Line Test

Question 6

Use the horizontal line test to determine whether the inverse of the graph is a function.

Accepted Answer

Not a Function

Answer

Function

Question 7

What is the inverse of the given quadratic function? $$f\left(x\right)=4\left(x+3\right)^2$$ when $$x\ge-3$$

Accepted Answer

$$f^{-1}\left(x\right)=\frac{\sqrt{x}}{2}-3$$

Answer

$$f^{-1}\left(x\right)=-4\left(x-3\right)^2$$

Answer

$$f^{-1}\left(x\right)=\sqrt{4x+3}$$

Answer

$$f^{-1}\left(x\right)=2\sqrt{x}-3$$

Question 8

Which function would need a domain restriction to ensure that its inverse is a function?

Accepted Answer

$$f\left(x\right)=x^2-16$$

Answer

$$f\left(x\right)=x^3$$

Answer

$$f\left(x\right)=\sqrt[]{x+2}-5$$

Answer

$$f\left(x\right)=2\left(x-6\right)-1$$

Question 9

To which intervals could we restrict the domain of f(x) to make it an invertible function? Choose all answers that apply.

Accepted Answer

[0, inf)

Accepted Answer

(-inf, 0]

Answer

[-4, 4]

Answer

none of the above

Question 10

Find the inverse function of $$y=\sqrt{x+11}$$

Accepted Answer

$$y=x^2-11$$

Answer

$$y=x^2+11$$

Answer

$$y=\left(x+11\right)^2$$

Answer

$$y=\left(x-11\right)^2$$

Question 11

Find the inverse function of $$f\left(x\right)=\sqrt{x}-6$$

Accepted Answer

$$y=\left(x+6\right)^2$$

Answer

$$y=\left(x-6\right)^2$$

Answer

$$y=x^2+6$$

Answer

$$y=x^2+36$$

Question 12

You restrict the domain when...

Accepted Answer

The inverse is not a function

Answer

The inverse is a function

1.4 Inverse of Quadratics Scholars

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