Question 1

Which of the following describes the transformation from $$y = \sqrt{x} to$$ $$y = \sqrt{x} + 2$$?

Accepted Answer

A vertical shift 2 units up

Question 2

Given $$y = |x|$$, what is the equation of the graph shifted 2 units to the left?

Accepted Answer

$$y = |x + 2|$$

Question 3

If $$f(x) = x^2$, which transformation results in g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units, then up 2 units

Question 4

Which of the following represents a vertical stretch of $$y = \sqrt{x} by a $$factor of 2?

Accepted Answer

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

Question 5

What is the effect of replacing $$x$$ with $$2x in $$the function $$y = f(x)$$?

Accepted Answer

Horizontal compression by a factor of $$\frac{1}{2}$$

Question 6

Given $$y = x^2$, which transformation results in y$$ = $$-x^2$$?

Accepted Answer

Reflection about the x-axis

Question 7

If $$f(x) = \sqrt{x}$$, what is the domain of $$g(x) = \sqrt{x-2}$$?

Accepted Answer

$$x \geq 2$$

Question 8

Which transformation is applied to $$y = x^2$ to obtain y$$ = \frac{1}{2}$$x^2$$?

Accepted Answer

Vertical compression by a factor of $$\frac{1}{2}$$

Question 9

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

Accepted Answer

Reflect about the x-axis, shift left 2 units, shift up 1 unit

Question 10

If $$f(x) = x^2$, what is the range of g(x$$) = $$x^2 + 1$?

Accepted Answer

$$y \geq 1$$

Question 11

A function $$f(x) is $$reflected about the y-axis. Which of the following is the correct transformation?

Accepted Answer

$$y = f(-x)$$

Question 12

Which transformation would change $$y = |x| to$$ $$y = |x| - 3$$?

Accepted Answer

Vertical shift down 3 units

Question 13

Given $$f(x) = x^2$, what is the equation after reflecting about the x-axis and shifting down 2 units?

Accepted Answer

$$y = -x^2$ - 2$$

Question 14

If $$f(x) = \sqrt{x}$$, which transformation results in $$g(x) = \sqrt{x+3} - 2$$?

Accepted Answer

Shift left 3 units, then down 2 units

Question 15

Which of the following is the result of a horizontal stretch by a factor of 2 applied to $$y = f(x)$$?

Accepted Answer

$$y = f\left(\frac{x}{2}\right)$$

Question 16

A real-world scenario: The height $$h (in $$meters) of a bouncing ball at time $$t (in $$seconds) is modeled by $$h(t) = -4.9t^2$ + 10. If $$the ball is dropped from a platform 3 meters higher, what is the new height function?

Accepted Answer

$$h(t) = -4.9t^2$ + 13$$

Question 17

If $$f(x) = x^2$, what is the effect of the transformation g(x$$) = $$(x+2)^2 - 1$?

Accepted Answer

Shift left 2 units, then down 1 unit

Question 18

Given $$f(x) = x^2$, which transformation results in g(x$$) = $$-2x^2 + 3$?

Accepted Answer

Reflect about the x-axis, vertical stretch by 2, shift up 3 units

Question 19

If $$f(x) = \sqrt{x}$$, what is the range of $$g(x) = -\sqrt{x}$$?

Accepted Answer

$$y \leq 0$$

Graphing Techniques: Transformations of Functions in Precalculus

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