Question 1

Given the function $$f(x) = \sqrt{x} - 3$$, which of the following describes the transformation applied to the parent function $$y = \sqrt{x}$$?

Accepted Answer

A vertical shift downward by 3 units

Question 2

What is the domain of the function $$f(x) = \sqrt{x} - 3$$?

Accepted Answer

$$x \geq 0$$

Question 3

What is the range of the function $$f(x) = \sqrt{x} - 3$$?

Accepted Answer

$$y \geq -3$$

Question 4

Which point lies on the graph of $$f(x) = \sqrt{x} - 3$$?

Accepted Answer

$$(4, -1)$$

Question 5

If the function $$f(x) = \sqrt{x} - 3$$ models the height (in meters) of a plant $$x$$ days after planting, what is the initial height of the plant?

Accepted Answer

$$-3$$ meters

Question 6

Which of the following best describes the end behavior of $$f(x) = \sqrt{x} - 3 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 7

Suppose $$g(x) = \sqrt{x - 2} - 3. $$How does the graph of $$g(x)$$ compare to $$f(x) = \sqrt{x} - 3$$?

Accepted Answer

It is shifted 2 units to the right

Question 8

If $$f(x) = \sqrt{x} - 3$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 9$$

Question 9

Which of the following is the inverse of $$f(x) = \sqrt{x} - 3$$?

Accepted Answer

$$f^{-1}(x) = (x$$ + $$3)^2$$

Question 10

If $$f(x) = \sqrt{x} - 3$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$(9, 0)$$

Question 11

A scientist uses $$f(x) = \sqrt{x} - 3 to $$model the temperature change in a reaction over time $$x (in $$minutes). After how many minutes will the temperature change reach $$2$$ degrees?

Accepted Answer

$$25$$ minutes

Question 12

Which of the following statements is true about the graph of $$f(x) = \sqrt{x} - 3$$?

Accepted Answer

The graph starts at $$(0, -3)$$ and increases without bound

Graphing Functions Using Transformations: Square Root Functions

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