$$x \in \mathbb{R}, x \geq 5, x \neq 0$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-5} / x$$?

Accepted Answer

$$x \in \mathbb{R}, x \geq 5, x 
eq 0$$

Question 2

A function $$f: \mathbb{R} 	o \mathbb{R} is $$called even if:

Accepted Answer

$$f(-x) = f(x)$$ for all $$x \in \mathbb{R}$$

Question 3

Which of the following is NOT a way to represent a function?

Accepted Answer

A histogram

Question 4

The Vertical Line Test (VLT) is used to:

Accepted Answer

Determine if a set of points represents a function

Question 5

Which of the following functions is transcendental?

Accepted Answer

$$f(x) = e^x$$

Question 6

Given the piecewise function $$f(x) = \begin{cases} x^2$ & x \u003c 1 \ 2-x & 1 \leq x \u003c 3 \ x-1 & x \geq 3 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$f(2) = 0$$

Question 7

Which of the following statements about the codomain and range of a function is correct?

Accepted Answer

The range is always a subset of the codomain

Question 8

Which of the following is an example of a periodic function?

Accepted Answer

$$f(x) = \sin(x)$$

Question 9

Suppose $$f(x) = |x|. $$Which of the following is true?

Accepted Answer

$$f(x) is an $$even function

Question 10

Which of the following best describes a composite function?

Accepted Answer

A function formed by applying one function to the result of another function

Question 11

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

Accepted Answer

$$x \leq 0 or$$ $$x \geq 4$$

Question 12

Which of the following is true about the function $$f(x) = \sin(x)$$?

Accepted Answer

$$f(x) is $$odd

Question 13

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

Accepted Answer

$$f(x_1$) \u003e f(x_2$)$$ for all $$x_1$$ \u003c $$x_2$$

Question 14

Which of the following is a real-world application of piecewise functions?

Accepted Answer

Modeling the cost of electricity with different rates for different usage levels

Question 15

If $$|2x + 6| \geq 8$$, what is the solution set for $$x$$?

Accepted Answer

$$x \leq -7 or$$ $$x \geq 1$$

Question 16

Which of the following is NOT a characteristic of algebraic functions?

Accepted Answer

They include exponential and logarithmic functions

Question 17

Which of the following best describes the range of $$f(x) = \sqrt{x-5}/x$$?

Accepted Answer

$$0 \u003c y \leq 1/\sqrt{5}$$, y \in \mathbb{R}$

Question 18

Which of the following is true about the absolute value function $$f(x) = |x|$$?

Accepted Answer

It is a piecewise function

Question 19

Which of the following is a logarithmic function?

Accepted Answer

$$f(x) = \ln(x)$$

Review and Basic Classes of Functions – MAT135 Differential Calculus (University of Toronto Mississauga)

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