Functions and Relations

Question 1

What is a function?

Answer 1

A relation that assigns exactly one output for each input.

Question 2

True or False: A function can have multiple outputs for a single input.

Answer 2

False

Question 3

What is the domain of a function?

Answer 3

The set of all possible input values.

Question 4

What is the range of a function?

Answer 4

The set of all possible output values.

Question 5

Fill in the blank: A function is often denoted by a ______.

Answer 5

letter, such as f, g, or h.

Question 6

What is the difference between a function and a relation?

Answer 6

A function is a specific type of relation where each input has exactly one output.

Question 7

True or False: All functions are relations, but not all relations are functions.

Answer 7

True

Question 8

What is an independent variable?

Answer 8

The variable that represents the input of a function.

Question 9

What is a dependent variable?

Answer 9

The variable that represents the output of a function.

Question 10

Fill in the blank: A function can be represented graphically as a ______.

Answer 10

curve or line on a coordinate plane.

Question 11

What is a composite function?

Answer 11

A function created by combining two functions, denoted as (f ∘ g)(x) = f(g(x)).

Question 12

True or False: The notation f(x) means the output of function f for the input x.

Answer 12

True

Question 13

What is an inverse function?

Answer 13

A function that reverses the effect of the original function.

Question 14

What is a vertical line test?

Answer 14

A method to determine if a relation is a function by checking if any vertical line intersects the graph more than once.

Question 15

What does it mean for a function to be continuous?

Answer 15

The function has no breaks, jumps, or holes in its graph.

Question 16

Fill in the blank: A linear function can be expressed in the form y = ______.

Answer 16

mx + b.

Question 17

What is a quadratic function?

Answer 17

A function that can be expressed in the form y = ax² + bx + c.

Question 18

What is the leading coefficient of a polynomial?

Answer 18

The coefficient of the term with the highest degree.

Question 19

True or False: The graph of a quadratic function is always a straight line.

Answer 19

False

Question 20

Does the graph of a vertical line represent a function?

Answer 20

No, it does not represent a function.

Question 21

What is the vertical line test used for?

Answer 21

To determine if a graph represents a function.

Question 22

True or False: A graph that passes the vertical line test represents a function.

Answer 22

True.

Question 23

Fill in the blank: A function must have _____ output for each input.

Answer 23

exactly one

Question 24

Does the graph of the equation y = x^2 represent a function?

Answer 24

Yes, it represents a function.

Question 25

What type of graph typically represents a function?

Answer 25

A graph where each x-value has only one corresponding y-value.

Question 26

Multiple Choice: Which of the following graphs represents a function? A) A circle B) A parabola C) A vertical line

Answer 26

B) A parabola.

Question 27

Is the graph of the equation x + y = 1 a function?

Answer 27

No, it is not a function.

Question 28

Short Answer: What does it mean for a graph to not represent a function?

Answer 28

It means that at least one x-value has more than one y-value.

Question 29

True or False: A horizontal line can represent a function.

Answer 29

True.