Question 1

Which of the following rules does NOT define a function from the set of people to the set of birthdays?

Accepted Answer

The rule that assigns to each birthday the person or people with that birthday.

Question 2

Given the function $$f(x) = x^2$ + 3x + 5$$, what is the value of $$f(1)$$?

Accepted Answer

$$9$$

Question 3

A cell phone company offers a plan where $$C(x) = \begin{cases} 40 & 	ext{if } 0 \leq x \leq 15 \ 40 + 0.60(x - 15) & 	ext{if } x \u003e 15 \end{cases}$$, where $$x is $$the number of GB used. What is the cost for using 20 GB?

Accepted Answer

$$43.00$$

Question 4

Which graph passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upwards

Question 5

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

Accepted Answer

$$x \in \mathbb{R}$$

Question 6

Find the inverse of the function $$f(x) = 3x + 2.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 2}{3}$$

Question 7

Express $$(3 + 5i) + (4 - 2i) in $$standard form.

Accepted Answer

$$7 + 3i$$

Question 8

Solve the quadratic equation $$x^2 + 4x + 5 = 0$ for x$.

Accepted Answer

$$x = -2 \pm i$$

Question 9

Which of the following is the correct vertex form for the quadratic function $$f(x) = x^2$ - 4x + 3$$?

Accepted Answer

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

Question 10

An archer's arrow follows a parabolic path modeled by $$f(x) = -0.05x^2$ + 2x + 5$$, where $$x is $$the horizontal distance in feet. What is the maximum height of the arrow?

Accepted Answer

$$13$$

Question 11

Given the piecewise function $$f(x) = \begin{cases} x + 2 & x \leq 1 \ 4 & x \u003e 1 \end{cases}$$, what is $$f(0)$$?

Accepted Answer

$$2$$

Question 12

If $$z = 3 - 4i$$, what is the modulus $$|z|$$?

Accepted Answer

$$5$$

Question 13

Which of the following is the correct composition $$f(g(x)) if$$ $$f(x) = x^2$ and g(x) = x + 1$?

Accepted Answer

$$(x + 1)^2$

Question 14

A computer store offers a 15% discount on all computers. If the regular price is $$P$$, what is the function $$f(P)$$ representing the sale price?

Accepted Answer

$$f(P) = 0.85P$$

Question 15

Which of the following is the correct inverse of $$f(x) = \frac{x + 2}{x - 3}$$?

Accepted Answer

Question 16

Simplify $$\sqrt{-25}$$ using complex numbers.

Accepted Answer

$$5i$$

Question 17

Which of the following statements about the domain of a composite function $$f(g(x)) is $$correct?

Accepted Answer

It is the set of all $$x in $$the domain of $$g$$ such that $$g(x) is in $$the domain of $$f.$$

Question 18

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of g(f(x$$))$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 19

Given the quadratic function $$f(x) = -2x^2$ + 6x - 13$$, does it have a maximum or minimum value, and what is that value?

Accepted Answer

Maximum value at $$x = 1.5$$, $$f(1.5) = -8.5$$

Question 20

Which of the following is the correct standard form for the product $$(3 + 5i)(4 - 2i)$$?

Accepted Answer

$$22 + 14i$$

Precalculus Study Notes: Functions, Piecewise Functions, Graphs, Complex Numbers, and Quadratic Functions

Guida di studio - Domande di pratica

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