Question 1

Which transformation is applied to the basic function $$y = x^2$ to obtain f(x) = (x$$ + $$2)^2 - 3$?

Accepted Answer

Shift left 2 units and down 3 units

Question 2

What is the domain and range of $$f(x) = 3(x-2)^2$ + 1$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[1, \infty)$$

Question 3

Which of the following describes the transformation from $$y = |x| to$$ $$g(x) = 3|x+1| - 3$$?

Accepted Answer

Vertical stretch by 3, shift left 1, shift down 3

Question 4

Given $$h(x) = \frac{4}{x} + 2$$, what is the vertical asymptote?

Accepted Answer

$$x = 0$$

Question 5

What is the effect of the transformation $$f(x) 	o f(x+2) on $$the graph of $$f(x)$$?

Accepted Answer

Shift left 2 units

Question 6

If $$f(x) = x^2$, what is the graph of P(x) = -f(x$$)$$?

Accepted Answer

Reflection of $$f(x)$$ over the $$x-$$axis

Question 7

Which function represents a vertical compression of $$f(x) by a $$factor of $$\frac{1}{2}$$?

Accepted Answer

$$Q(x) = \frac{1}{2}f(x)$$

Question 8

Given $$g(x) = 4\sqrt{2-x}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$(-\infty, 2]$$

Question 9

If $$f(x) is a $$function, what does $$f(-x) do to $$its graph?

Accepted Answer

Reflects it over the $$y-$$axis

Question 10

Which of the following is the correct transformation for $$H(x) = f(x+1) - 2$$?

Accepted Answer

Shift left 1 unit, down 2 units

Question 11

Given $$f(x) = -(x+1)^3$ - 1$$, what is the sequence of transformations from $$y = x^3$?

Accepted Answer

Shift left 1, reflect over $$x-$$axis, shift down 1

Question 12

If $$F(x) = f(x) + 3$$, what is the effect on the graph of $$f(x)$$?

Accepted Answer

Shift up 3 units

Question 13

Which transformation results in a horizontal compression by a factor of 2?

Accepted Answer

$$h(x) = f(2x)$$

Question 14

What is the range of $$h(x) = \frac{4}{x} + 2$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 15

Which function transformation would shift the graph of $$f(x)$$ down by 2 units and left by 1 unit?

Accepted Answer

$$H(x) = f(x+1) - 2$$

Precalculus Function Transformations and Graphing Guidance

Study Guide - Practice Questions