Question 1

Which of the following best describes a function?

Accepted Answer

A rule that assigns each element of the domain to exactly one element of the range.

Question 2

Given the set of ordered pairs $$\{(-5, -7), (-3, -2), (-1, 6), (0, -2), (3, 5), (5, -7)\}$$, what is the domain?

Accepted Answer

$$\{-5, -3, -1, 0, 3, 5\}$$

Question 3

A thermometer reads $$37^\circC. $$Using the formula $$F = \frac{9}{5}C + 32$$, what is the temperature in Fahrenheit?

Accepted Answer

$$F = 98.6$$

Question 4

Which of the following relationships is NOT a function?

Accepted Answer

Some inputs have more than one output.

Question 5

Given the function $$f(x) = 2x^3$ + 5x^2$ - 28x - 15$$, what is $$f(2)$$?

Accepted Answer

$$f(2) = 45$$

Question 6

A graph passes the vertical line test if:

Accepted Answer

No vertical line intersects the graph at more than one point.

Question 7

The function $$V(t) = 3.77t^2$ + 24.4t + 131.9$$ models the value of the medical 3D printing market (in millions of dollars), where $$t is $$the number of years after 2010. What is the projected value in 2027?

Accepted Answer

$$V(17) = 1609.9$$

Question 8

If a table lists the number of female physicians in the U.S. for each year from 2015 to 2040, is this relationship a function?

Accepted Answer

Yes, because each year corresponds to exactly one number of physicians.

Question 9

Given the function $$g(t)$$ representing the number of older men in the workforce (in millions) as a function of year $$t$$, if $$g(2020) = 21$$, what does this mean?

Accepted Answer

There were 21 million older men in the workforce in 2020.

Question 10

For the function $$V(t) = 3.77t^2$ + 24.4t + 131.9$$, what value of $$t$$ corresponds to the year 2025?

Accepted Answer

$$t = 15$$

Question 11

Which of the following is the correct range for the function defined by the set $$\{(-5, -7), (-3, -2), (-1, 6), (0, -2), (3, 5), (5, -7)\}$$?

Accepted Answer

$$\{-7, -2, 6, 5\}$$

Question 12

If a graph continues indefinitely to the left and is bounded on the right at $$x = 4$$, what is the domain?

Accepted Answer

$$(-\infty, 4]$$

Question 13

Suppose $$f(x) = -x^2$ + 4x. Is$$ $$y a $$function of $$x$$?

Accepted Answer

Yes, because each $$x$$ gives exactly one $$y$$ value.

Question 14

A scatter plot is useful for which of the following purposes?

Accepted Answer

Visualizing the relationship between two variables using ordered pairs.

Question 15

If $$f(x) = 2x^3$ + 5x^2$ - 28x - 15$$, what is $$f(4)$$?

Accepted Answer

$$f(4) = 81$$

Question 16

If the number of older men in the workforce is modeled by $$g(t)$$ and $$g(2030) = 19.6$$, what is the input and what is the output?

Accepted Answer

Input: 2030, Output: 19.6

Question 17

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

Accepted Answer

The domain is the set of all possible input values, and the range is the set of all possible output values.

Question 18

If a function is defined by a table where each input year is listed only once, what can you conclude?

Accepted Answer

The relationship is a function.

Question 19

If the value of the medical 3D printing market in 2025 is projected to be $$V(15) = 1319.9$$ million dollars, what does this mean in context?

Accepted Answer

In 2025, the market is projected to be approximately $$1.32$$ billion dollars.

College Algebra: Functions, Graphs, and Models – Study Notes

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