Q: A real-world scenario: The function $W(t)$ models the average American's weight gain in pounds after $t$ years of always ordering the larger portion. If $W(5) = 12$, what does this mean?

After 5 years, the average American will have gained 12 pounds.

Q: Given the interval $x < -2$ or $x \\geq 5$, what is the interval notation?

$(-5cinfty, -2) \\cup [5, 5cinfty)$

Q: Suppose the function $StopDistance(x)$ gives the stopping distance in feet for a car traveling at $x$ mph. If $StopDistance(70) = 454$, what is the meaning of $StopDistance(70) = 454$?

A car traveling at 70 mph requires 454 feet to stop.

Question 1

Which of the following best describes the definition of a function?

Accepted Answer

A relation in which each input is paired with exactly one output.

Question 2

Given the table below, is the relation a function?

$x$ | $1$ | $3$ | $1$ | $5$
$y$ | $2$ | $6$ | $9$ | $7$

Accepted Answer

No, because the input $x=1$ is paired with two different outputs.

Question 3

What is the domain of the Median Income function shown in the study material?

Accepted Answer

The set of all states listed: Alabama, Indiana, Alaska, Colorado, Illinois, Massachusetts.

Question 4

Given the function $f(x) = -5x + 1$, what is $f(-3)$?

Accepted Answer

$16$

Question 5

Which of the following equations does NOT represent $y$ as a function of $x$?

Accepted Answer

$x = y^2$

Question 6

A vehicle's stopping distance is given in the table below:

Speed (MPH): $30$, $40$, $50$, $60$, $70$
Stopping Distance (ft): $109$, $173$, $253$, $346$, $454$

What is $StopDistance(40)$?

Accepted Answer

$173$

Question 7

Given the function $Complement(x) = 90 - x$, what is $Complement(88)$?

Accepted Answer

$2$

Question 8

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

Accepted Answer

A graph where every vertical line crosses the curve at most once.

Question 9

What is the interval notation for the solution set $-4 < x \leq 8$?

Accepted Answer

$(-4, 8]$

Question 10

If $f(x) = |x + 1|$, what is $f(-3)$?

Accepted Answer

$2$

Question 11

Given the function $f(x) = -5x + 1$, what is $-f(x+3)$?

Accepted Answer

$5x + 16$

Question 12

Which of the following best describes the range of the function $y = x^2 - 3$?

Accepted Answer

$[-3, \infty)$

Question 13

A real-world scenario: The function $W(t)$ models the average American's weight gain in pounds after $t$ years of always ordering the larger portion. If $W(5) = 12$, what does this mean?

Accepted Answer

After 5 years, the average American will have gained 12 pounds.

Question 14

Given the interval $x < -2$ or $x \geq 5$, what is the interval notation?

Accepted Answer

$(- 5cinfty, -2) \cup [5,  5cinfty)$

Question 15

Suppose the function $StopDistance(x)$ gives the stopping distance in feet for a car traveling at $x$ mph. If $StopDistance(70) = 454$, what is the meaning of $StopDistance(70) = 454$?

Accepted Answer

A car traveling at 70 mph requires 454 feet to stop.

Question 16

Which of the following is the correct interval notation for $x > -1$?

Accepted Answer

$(-1,  5cinfty)$

Question 17

If the function $f(x)$ is defined by the graph below and $f(-1) = 2$, what does this mean?

Accepted Answer

When $x = -1$, the output of the function is $2$.

Question 18

Which of the following best describes the range of the Median Income function from the study material?

Accepted Answer

The set of all median incomes listed: $55, 65, 72, 83$

Question 19

Given the function $Complement(x) = 90 - x$, what is the domain of this function if $x$ represents the measure of an angle in degrees?

Accepted Answer

$[0, 90]$

Functions and Their Representations: College Algebra Study Notes

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