Question 1

Which of the following best describes a function?

Accepted Answer

A relation in which each possible input value leads to exactly one output value.

Question 2

Given the graph of a circle $$x^2$$ + $$y^2 = 9$, does this graph represent a function?

Accepted Answer

No, because some $$x$$ values correspond to more than one $$y$$ value.

Question 3

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$y = x^2$

Question 4

A vertical line intersects a graph at more than one point. What does this indicate about the graph?

Accepted Answer

The graph does not represent a function.

Question 5

Given the equation $$y = \pm \sqrt{x + 2}$$, does this equation define $$y as a $$function of $$x$$?

Accepted Answer

No, because for some $$x$$ there are two possible $$y$$ values.

Question 6

Suppose $$f is $$graphed below and $$f(3) = 1. $$What does this mean?

Accepted Answer

When $$x = 3$$, $$f(x) = 1.$$

Question 7

If $$f(x) = 40$$ and the table below shows $$f(80) = 40$$, what is the value of $$x$$?

Accepted Answer

$$x = 80$$

Question 8

Which of the following is NOT a function?

Accepted Answer

$$x = y^2$

Question 9

A student claims that the graph of $$y = x^2$ passes the vertical line test. Is this correct?

Accepted Answer

Yes, because every vertical line intersects the graph at most once.

Question 10

Which statement about the predictability of functions is correct?

Accepted Answer

Functions are predictable because each input has exactly one output.

Question 11

Given the table below, if $$f(0) = 60$$, what is the output when the input is $$0$$?

Accepted Answer

$$60$$

Question 12

If a graph fails the vertical line test, what does this mean in terms of functions?

Accepted Answer

The graph does not represent a function.

Question 13

Suppose you are given the graph of $$y = x^2$ and x$$ = $$y^2. $$Which graph represents $$y as a $$function of $$x$$?

Accepted Answer

$$y = x^2$

Question 14

A hospital tracks patient temperature over time. If each time value is paired with exactly one temperature, is this a function?

Accepted Answer

Yes, because each time value has exactly one temperature.

Question 15

Which of the following real-world scenarios is NOT a function?

Accepted Answer

Assigning each book to multiple library shelves.

Question 16

If $$f(x) is $$graphed and $$f(x) = -6 at$$ $$x = 7$$, what is the value of $$f(7)$$?

Accepted Answer

$$-6$$

Question 17

Which of the following is a valid way to determine if a graph represents a function?

Accepted Answer

Check if any vertical line intersects the graph more than once.

Question 18

A chemical reaction is monitored, and for each minute, the concentration of a reactant is recorded. Is this a function?

Accepted Answer

Yes, because each minute has exactly one concentration value.

Question 19

If $$f(x) is $$defined by the table and $$f(50) = 40$$, what is the input value for which the output is $$40$$?

Accepted Answer

$$x = 50$$

Question 20

Which of the following best explains why $$x = y^2$ does NOT define y$ as a function of x$?

Accepted Answer

Because for some $$x$$ values, there are two possible $$y$$ values.

Introduction to Functions: Definitions, Graphs, and Tables

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