Question 1

Which transformation will shift the graph of $$y = \sqrt{x} up by 2 $$units?

Accepted Answer

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

Question 2

Given the function $$f(x) = |x|$$, what is the equation of the graph shifted 2 units to the right?

Accepted Answer

$$f(x) = |x - 2|$$

Question 3

If $$g(x) = x^2$, which transformation results in a vertical compression by a factor of $$\frac{1}{2}$$?

Accepted Answer

$$g(x) = \frac{1}{2}x^2$

Question 4

What is the effect of replacing $$x$$ with $$x - 3 in $$the function $$f(x) = x^2$?

Accepted Answer

Shifts the graph 3 units to the right

Question 5

Which of the following describes the transformation from $$y = x^2$ to y = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units, then up 2 units

Question 6

If $$f(x) = \sqrt{x}$$, what is the equation for the graph reflected about the $$x-$$axis?

Accepted Answer

$$f(x) = -\sqrt{x}$$

Question 7

A function $$f(x) is $$horizontally compressed by a factor of 2. Which equation represents this transformation?

Accepted Answer

$$f(2x)$$

Question 8

Given $$f(x) = x^2$, which transformation results in f(x$$) = $$x^2 + 1$?

Accepted Answer

Vertical shift up 1 unit

Question 9

Which of the following is the result of reflecting $$y = x^3$ about the y$-axis?

Accepted Answer

$$y = (-x)^3$

Question 10

A medical researcher models the spread of a virus with $$f(x) = \sqrt{x}. If $$the initial data is delayed by 2 days, which function models the new data?

Accepted Answer

$$f(x - 2) = \sqrt{x - 2}$$

Question 11

Which transformation will reflect the graph of $$y = \sqrt{x}$$ about the $$y-$$axis?

Accepted Answer

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

Question 12

If $$f(x) = x^2$, what is the result of applying the following transformations in order: shift right 3 units, reflect about the x$-axis, shift down 2 units?

Accepted Answer

$$f(x) = -(x - 3)^2$ - 2$$

Question 13

A company’s profit is modeled by $$f(x) = x^2$. If the profit is doubled and then shifted up by 1 unit, what is the new function?

Accepted Answer

$$f(x) = 2x^2$ + 1$$

Question 14

Which transformation sequence will produce $$y = -\sqrt{x + 2} + 1$$ from $$y = \sqrt{x}$$?

Accepted Answer

Shift left 2 units, reflect about the $$x-$$axis, shift up 1 unit

Question 15

If $$f(x) = x^2$, what is the effect of multiplying the input by $$\frac{1}{2}$$, i.e., f$$\left(\frac{x}{2}\right)$$?

Accepted Answer

Horizontal stretch by a factor of 2

Question 16

A population model is given by $$f(x) = x^2$. If the population is expected to decrease by 2 units at every value of x$, what is the new function?

Accepted Answer

$$f(x) = x^2$ - 2$$

Question 17

Which of the following is the result of reflecting $$y = \sqrt{x}$$ about the $$x-$$axis and then shifting it down 2 units?

Accepted Answer

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

Question 18

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

Accepted Answer

Shift left 2 units

Question 19

A sound wave is modeled by $$f(x) = \sin(x). If $$the wave is horizontally compressed by a factor of 2, what is the new function?

Accepted Answer

$$f(2x) = \sin(2x)$$

Graphing Techniques: Transformations of Functions

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