Question 1

Which of the following best describes the symmetry of the graph of $$f(x) = x^2$?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 2

A function $$f is $$defined as $$f(x) = 2x + 3. $$Which of the following statements is true about its graph?

Accepted Answer

The graph is a straight line with slope $$2$$ and $$y-$$intercept $$3.$$

Question 3

Which property must a function $$f(x)$$ satisfy to be classified as an even function?

Accepted Answer

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

Question 4

Suppose the graph of $$y = f(x)$$ passes the vertical line test. What does this indicate about $$f$$?

Accepted Answer

$$f is a $$function.

Question 5

Given $$f(x) = |x|$$, which of the following statements is true about its graph?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 6

If $$f(x) = x^3$, which of the following is true about its symmetry?

Accepted Answer

It is an odd function.

Question 7

A function $$f is $$defined as $$f(x) = 4 - x^2$. What is the y$-intercept of its graph?

Accepted Answer

$$y = 4$$

Question 8

Which of the following describes the effect of replacing $$x$$ with $$x - 2 in $$the function $$f(x)$$?

Accepted Answer

The graph shifts $$2$$ units to the right.

Question 9

If $$f(x) = x^2$ and g(x) = f(x) + 5$, what is the y$-intercept of g(x$$)$$?

Accepted Answer

$$y = 5$$

Question 10

A function $$f(x) is $$reflected across the $$x-$$axis. Which transformation represents this?

Accepted Answer

$$f(x) 	o -f(x)$$

Question 11

Which of the following is the domain of $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

$$x \geq 3$$

Question 12

If $$f(x) = x^2$ and g(x) = f(-x$$)$$, what is the relationship between f$ and g$?

Accepted Answer

They are identical functions.

Question 13

A population of bacteria grows according to $$P(t) = 500e$$^{0.2t}$$. What is the population after 5$ hours?

Accepted Answer

$$P(5) = 500e$$^{1}$$

Question 14

Which of the following is the range of $$f(x) = \frac{1}{x}$$?

Accepted Answer

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

Question 15

If $$f(x) = x^2$ and g(x) = 3f(x$$)$$, what happens to the graph of f(x$$)$$?

Accepted Answer

It is stretched vertically by a factor of $$3.$$

Question 16

A function $$f(x) is $$defined as $$f(x) = \sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$-3 \leq x \leq 3$$

Question 17

Which of the following transformations will shift the graph of $$f(x)$$ downward by $$4$$ units?

Accepted Answer

$$f(x) 	o f(x) - 4$$

Question 18

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

Accepted Answer

$$( -2, 0 )$$

Question 19

A function $$f(x) is $$defined as $$f(x) = \frac{1}{x - 2}. $$What is the vertical asymptote of its graph?

Accepted Answer

$$x = 2$$

Functions and Their Graphs: Key Concepts and Properties

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