Question 1

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

Accepted Answer

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

Question 2

Given the piecewise function $$C(x) = \begin{cases} 40 & 	ext{if } 0 \leq x \leq 15 \ 40 + 0.60(x-15) & 	ext{if } x \u003e 15 \end{cases}$$, what is $$C(20)$$?

Accepted Answer

$$43$$

Question 3

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

Accepted Answer

A standard upward-opening parabola.

Question 4

Suppose the value of a car is given by $$V(t) = 24.975 - 1.83t$$, where $$t is $$the age in years. What is the approximate value of the car when it is 3 years old?

Accepted Answer

$$19.485$$

Question 5

Let $$f(x) = x^2$ + 4$$ and $$g(x) = \sqrt{7 - x}. $$What is the domain of $$g(f(x))$$?

Accepted Answer

$$x^2 + 4$$ \leq 7 \implies $$x^2$$ \leq 3 \implies -\sqrt{3} \leq x \leq \sqrt{3}$$

Question 6

If $$f(x) = 3x + 2$$ and $$g(x) = \frac{x-2}{3}$$, what is $$f(g(x))$$?

Accepted Answer

$$x$$

Question 7

Which of the following is the inverse of $$f(x) = 7x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{7}$$

Question 8

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

Accepted Answer

$$7 + 3i$$

Question 9

Simplify $$\sqrt{-27}.$$

Accepted Answer

$$3i\sqrt{3}$$

Question 10

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$x = -\frac{b}{2a}. $$For $$f(x) = -2x^2$ + 6x - 13$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 1.5$$

Question 11

Given $$f(x) = x^2$ + 3x + 5$$, what is the vertex form of this quadratic function?

Accepted Answer

$$f(x) = (x + 1.5)^2$ + 2.75$$

Question 12

A cell phone company charges $$C(x) = 40 + 0.60(x-15)$$ for $$x \u003e 15 GB of $$data. How much will a customer pay for 25 GB of data?

Accepted Answer

$$52$$

Question 13

Which of the following is a correct interpretation of the statement $$g(5) = 15.975$$ for the function $$g(t)$$ representing the value of a car in thousands of dollars after $$t$$ years?

Accepted Answer

The value of the car is $$15,975$$ when it is $$5$$ years old.

Question 14

If $$f(x) = x^2$ + 2$$ for $$x \leq 1$$ and $$f(x) = 4$$ for $$x \u003e 1$$, what is $$f(2)$$?

Accepted Answer

$$4$$

Question 15

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

Accepted Answer

Question 16

Which of the following statements about the composition of functions is TRUE?

Accepted Answer

The domain of $$f \circ g is $$all $$x in $$the domain of $$g$$ such that $$g(x) is in $$the domain of $$f.$$

Question 17

A professor posts students' final exam grades by their student ID number. If two students have the same grade, is the relation from ID to grade a function?

Accepted Answer

Yes, because each ID is assigned to exactly one grade.

Question 18

Which of the following is the correct simplified form of $$\frac{3 + 5i}{1 - 2i}$$?

Accepted Answer

$$-1 + i$$

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

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