Question 1

Which transformation is applied to the parent function $$y = \sqrt{x} to $$obtain the function $$y = -\sqrt{x}$$?

Accepted Answer

Reflection in the x-axis

Question 2

Given the function $$y = \sqrt{-x}$$, what is its domain?

Accepted Answer

$$x \u003c 0$$

Question 3

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

Accepted Answer

$$y \u003c 0$$

Question 4

Which of the following describes the transformation for $$y = -\sqrt{x-2} + 1$$ compared to $$y = \sqrt{x}$$?

Accepted Answer

Reflection in the x-axis, shift right 2 units, up 1 unit

Question 5

For the function $$y = -3\sqrt{x+6} + 1$$, what is the domain?

Accepted Answer

$$x \geq -6$$

Question 6

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

Accepted Answer

$$y \leq 1$$

Question 7

If the graph of $$y = \sqrt{x} is $$reflected in the y-axis, what is the resulting equation?

Accepted Answer

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

Question 8

A medical researcher models the rate of drug absorption with $$y = 2\sqrt{x-1}. $$What is the minimum time $$x (in $$hours) after administration for absorption to begin?

Accepted Answer

$$x = 1$$

Question 9

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

Accepted Answer

Domain: $$x \geq 2$$, Range: $$y \geq 0$$

Question 10

A chemical reaction is modeled by $$y = -2\sqrt{x+3}. $$What is the effect of the coefficient -2?

Accepted Answer

Vertical stretch by 2 and reflection in the x-axis

Question 11

Which transformation sequence correctly maps $$y = \sqrt{x} to$$ $$y = \sqrt{-x-2}$$?

Accepted Answer

Reflect in y-axis, shift right 2 units

Question 12

If $$y = a\sqrt{x-h} + k$$, which parameter affects the horizontal shift of the graph?

Accepted Answer

$$h$$

Question 13

A population growth model uses $$y = \sqrt{2x+4}. $$What is the domain of this function?

Accepted Answer

$$x \geq -2$$

Question 14

Which of the following functions has a range $$y \leq 0$$?

Accepted Answer

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

Question 15

Given $$y = -\sqrt{2x-4} + 3$$, what is the vertex of the graph?

Accepted Answer

$$(2, 3)$$

Question 16

A scientist graphs $$y = 4\sqrt{x+1} - 2. $$What is the effect of the -2 in the equation?

Accepted Answer

Vertical shift down 2 units

Question 17

Which function represents a reflection in both the x-axis and y-axis of $$y = \sqrt{x}$$?

Accepted Answer

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

Question 18

For $$y = -2\sqrt{x-5} + 4$$, what is the domain and range?

Accepted Answer

Domain: $$x \geq 5$$, Range: $$y \leq 4$$

Question 19

A graph of $$y = \sqrt{x} is $$shifted 3 units up and 2 units right. What is the new equation?

Accepted Answer

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

Graphing Radical Functions Using Transformations

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