Question 1

Given the function $$y = -\sqrt{x}$$, which transformation is applied to the parent function $$y = \sqrt{x}$$?

Accepted Answer

Reflection in the x-axis

Question 2

What is the domain and range of the function $$y = \sqrt{x}$$?

Accepted Answer

Domain: $$x \geq 0$$, Range: $$y \geq 0$$

Question 3

Which of the following describes the transformation for $$y = \sqrt{-x}$$?

Accepted Answer

Reflection in the y-axis

Question 4

For the function $$y = -\sqrt{x-1} + 2$$, what is the domain?

Accepted Answer

$$x \geq 1$$

Question 5

Given $$y = -\sqrt{x-1} + 2$$, what is the range?

Accepted Answer

$$y \leq 2$$

Question 6

If the graph of $$y = \sqrt{x} is $$reflected in the y-axis and then shifted up by 3 units, what is the equation of the new function?

Accepted Answer

$$y = \sqrt{-x} + 3$$

Question 7

A function is given by $$y = -2\sqrt{x+4} - 5. $$Which of the following describes all the transformations applied to $$y = \sqrt{x}$$?

Accepted Answer

Vertical stretch by 2, reflection in x-axis, left shift by 4, down shift by 5

Question 8

What is the domain of $$y = \sqrt{2x-6}$$?

Accepted Answer

$$x \geq 3$$

Question 9

Given the function $$y = -3\sqrt{2x-6} + 1$$, what is the range?

Accepted Answer

$$y \leq 1$$

Question 10

A medical researcher models the rate of drug absorption in the bloodstream with $$y = \sqrt{t-2}$$, where $$t is $$time in hours. What is the earliest time $$t$$ for which the model is valid?

Accepted Answer

$$t = 2$$

Question 11

Which of the following is the correct domain for the function $$y = \sqrt{-x+5}$$?

Accepted Answer

$$x \leq 5$$

Question 12

If $$y = \sqrt{x} is $$transformed to $$y = \sqrt{x-3} + 2$$, what is the new vertex of the graph?

Accepted Answer

$$(3, 2)$$

Question 13

A chemical reaction rate is modeled by $$y = -\sqrt{x+2}. $$What is the range of possible reaction rates?

Accepted Answer

$$y \leq 0$$

Question 14

Which transformation occurs when $$y = \sqrt{x} is $$changed to $$y = \sqrt{x+5}$$?

Accepted Answer

Shift left by 5 units

Question 15

For the function $$y = -\sqrt{-x+4} + 3$$, what is the domain?

Accepted Answer

$$x \leq 4$$

Question 16

A function $$y = a\sqrt{x-h} + k is $$given. Which parameter controls the horizontal shift?

Accepted Answer

$$h$$

Question 17

If $$y = \sqrt{x} is $$reflected in the x-axis and shifted down by 4 units, what is the equation of the new function?

Accepted Answer

$$y = -\sqrt{x} - 4$$

Question 18

Which of the following is the correct range for $$y = \sqrt{x-2}$$?

Accepted Answer

$$y \geq 0$$

Question 19

A function $$y = -\sqrt{2x-6} + 1 is $$used to model the cooling of a substance. What is the minimum temperature predicted by the model?

Accepted Answer

$$y = 1$$

Question 20

Which of the following functions has a vertex at $$(2, -3)$$?

Accepted Answer

$$y = \sqrt{x-2} - 3$$

Graphing Radical Functions Using Transformations

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