Quiz about Domain & Range of Square Roots

Question 1

When looking at the square root vertex formula, $$f\left(x\right)=a\sqrt[]{x-h}+k$$ , what does k represent?

Accepted Answer

range, but don't flip #

Answer

domain, but flip # to get answer

Answer

range, but flip # to get answer

Answer

domain, but don't flip #

Question 2

When looking at the square root vertex formula, $$f\left(x\right)=a\sqrt[]{x-h}+k$$ , what does h represent?

Accepted Answer

domain, but flip # to get answer

Answer

range, but flip # to get answer

Answer

domain, but don't flip #

Answer

range, but don't flip #

Question 3

When looking at the square root vertex formula, $$f\left(x\right)=a\sqrt[]{x-h}+k$$ , what happens when a is negative?

Accepted Answer

y flips which means range is less than or equal to

Answer

nothing

Answer

x flips which means domain is less than or equal to

Answer

both x and y flip

Question 4

What is the DOMAIN of this square root function?

Accepted Answer

$$x\ge0$$

Answer

all real numbers

Answer

$$x\le0$$

Answer

$$y\ge0$$

Question 5

What is the RANGE of this square root function?

Accepted Answer

$$y\le2$$

Answer

all real numbers

Answer

$$y\ge1$$

Answer

$$y\ge2$$

Question 6

Which statement about the domain and range of both equations must be true?

Accepted Answer

The domain of the red curve is the same as the range of the red curve, all real numbers greater than or equal to 0, and the range of the red curve is the same as the restricted range of the blue curve, all real numbers greater than or equal to 0.

Answer

The domain of the red curve is the same as the range of the blue curve, all real numbers less than or equal to 0, and the range of the red curve is the same as the restricted domain of the blue curve, all real numbers less than or equal to 0.

Answer

The domain of the red curve is the same as the restricted domain of the blue curve, all real numbers less than or equal to 0, and the range of the red curve is the same as the range of the blue curve, all real numbers less than 0.

Answer

The domain of the red curve is the same as the restricted domain of the blue curve, all real numbers greater than or equal to 0, and the range of the red curve is the same as the range of the blue curve, all real numbers greater than or equal to 0.

Question 7

Let the function f be defined by $$f\left(x\right)=\sqrt[]{x-3}$$ , where $$x\ge3$$ . Which statements are true? Select TWO correct answers.

Accepted Answer

The inverse function of f is $$f^{-1}\left(x\right)=x^2+3$$

Accepted Answer

The domain of $$f^{-1}$$ is $$\left[0,\infty\right)$$

Answer

The inverse function of f is $$f^{-1}\left(x\right)=\left(x+3\right)^2$$

Answer

The inverse function of f is $$f^{-1}\left(x\right)=x^2-3$$

Answer

The domain of $$f^{-1}$$ is $$\left(\infty,\infty\right)$$

Question 8

When writing the domain and range in interval notation of a square root function, an exact number is denoted by what?

Accepted Answer

brackets

Answer

parenthesis

Answer

curly brackets

Answer

quotations

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