Question 1

Which of the following sets represents the range of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[0, \infty)$$

Question 2

Given the relation $$R = \{(1,2), (2,3), (3,4), (2,5)\}$$, is $$R a $$function?

Accepted Answer

No, because $$x=2 is $$paired with two different $$y-$$values.

Question 3

What is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 4

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A standard upward-opening parabola

Question 5

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain

Question 6

For the function $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

The function is odd.

Question 7

A function $$f is $$decreasing on an interval $$I if$$:

Accepted Answer

For any $$x_1  f$$($$x_2$$)$$

Question 8

Which transformation will shift the graph of $$f(x)$$ two units to the right?

Accepted Answer

$$f(x-2)$$

Question 9

Given $$f(x) = x^2$, what is the graph of g(x) = -f(x) + 3$?

Accepted Answer

The graph of $$f(x)$$ reflected across the $$x-$$axis and shifted up 3 units.

Question 10

Which of the following best describes the range of the reciprocal function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 11

If $$f(x) is $$increasing on $$(-\infty, 2)$$ and decreasing on $$(2, \infty)$$, what is true about $$x=2$$?

Accepted Answer

$$x=2 is a $$local maximum.

Question 12

Which of the following is the domain of the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

What is the effect of the transformation $$y = f(-x) on $$the graph of $$y = f(x)$$?

Accepted Answer

It reflects the graph across the $$y-$$axis.

Question 14

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

Accepted Answer

Shift left 3 units, down 2 units.

Question 15

Which of the following is NOT a function?

Accepted Answer

A mapping where an input is paired with two different outputs.

Question 16

If $$f(x) = x^2$ and g(x) = 2f(x$$)$$, what is the effect on the graph?

Accepted Answer

The graph is stretched vertically by a factor of 2.

Question 17

Which of the following intervals describes where the function $$f(x) is $$constant if $$f(x) = 5$$ for $$x \in [2,4]$$?

Accepted Answer

$$[2,4]$$

Question 18

Which of the following is the range of the square function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 19

If $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Functions and Their Graphs: Precalculus Study Notes

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