Q: A function $$f is $$said to be even if:

$$f(-x) = f(x)$$ \\text{ for all } x \\text{ in the domain}$

Q: A function $$f is $$odd if:

$$f(-x) = -f(x)$$ \\text{ for all } x \\text{ in the domain}$

Question 1

Which of the following statements correctly describes the x-intercepts of a function $$f(x)$$?

Accepted Answer

They are the points where $$f(x) = 0.$$

Question 2

Given the function $$f(x) = x^2$ - 4$$, what are the x-intercepts?

Accepted Answer

$$x = -2$$ and $$x = 2$$

Question 3

A function $$f is $$said to be even if:

Accepted Answer

$$f(-x) = f(x)$$ \text{ for all } x \text{ in the domain}$

Question 4

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 5

If a function $$f is $$increasing on the interval $$(a, b)$$, which of the following is true?

Accepted Answer

For any $$x_1$$ \u003c $$x_2 in$$ $$(a, b)$$, $$f(x_1$) \u003c f(x_2$)$$

Question 6

A function $$f is $$odd if:

Accepted Answer

$$f(-x) = -f(x)$$ \text{ for all } x \text{ in the domain}$

Question 7

Which of the following equations does NOT represent a function?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 8

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

Accepted Answer

$$x \geq 2$$

Question 9

A function $$f$$ has a relative maximum at $$x = c if$$:

Accepted Answer

$$f$$ changes from increasing to decreasing at $$x = c$$

Question 10

Which of the following best describes the range of the function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 11

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each element in the domain corresponds to exactly one element in the range.

Question 12

If the graph of a function passes the vertical line test, what does this indicate?

Accepted Answer

The graph represents a function.

Question 13

Given the function $$f(x) = \frac{x+1}{x-2}$$, which value is NOT in the domain?

Accepted Answer

$$x = 2$$

Question 14

Which of the following best describes the symmetry of the function $$f(x) = x^3$?

Accepted Answer

It is odd and symmetric about the origin.

Question 15

If two non-vertical lines in the Cartesian plane have the same slope, what can be concluded?

Accepted Answer

The lines are parallel.

Question 16

Which of the following is the correct formula for the difference quotient of a function $$f(x)$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 17

Given the function $$f(x) = x^2$ - 6x + 8$$, what is the y-intercept?

Accepted Answer

$$8$$

Question 18

Which of the following best describes the relationship between two perpendicular lines with slopes $$m_1$$ and $$m_2$$?

Accepted Answer

$$m_1$$ \cdot $$m_2 = -1$

Question 19

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is given by $$h(t) = -4.9t^2$ + 20t + 1.5$$, where $$t is $$time in seconds. At what time does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Precalculus Study Notes: Functions, Graphs, and Linear Relationships

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