Question 1

Given the function $$f(x) = 2x - 5$$, is the ordered pair $$(3, 1) a $$solution to the function equation?

Accepted Answer

Yes, because $$f(3) = 1$$

Question 2

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 3

A company charges a flat fee of $$\50$ plus $$\$$20$$ per hour for consulting. Which value represents the slope in the linear function that models the total cost $$C as a $$function of hours $$h$$?

Accepted Answer

$$20$$

Question 4

Which of the following is the correct graph for the equation $$y = -2x + 3$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$3$$

Question 5

Write the equation of the line passing through the points $$(1, 4)$$ and $$(3, 10) in $$slope-intercept form.

Accepted Answer

$$y = 3x + 1$$

Question 6

A biologist models the population of a bacteria culture with the function $$P(t) = 500 - 20t$$, where $$t is $$the number of hours since the start of the experiment. What does the slope represent in this context?

Accepted Answer

The population decreases by $$20$$ bacteria per hour.

Question 7

Find the domain of the function $$f(x) = \sqrt{x-7}.$$

Accepted Answer

$$[7, \infty)$$

Question 8

Which of the following ordered pairs is a solution to the equation $$y = 4x - 6$$?

Accepted Answer

$$(2, 2)$$

Question 9

A car rental company offers a plan that charges $$\30$ per day plus a one-time fee of $$\$$100. $$Write the equation for the total cost $$C as a $$function of the number of days $$d.$$

Accepted Answer

$$C = 30d + 100$$

Question 10

Given the function $$f(x) = \dfrac{2x+1}{x-2}$$, which value must be excluded from the domain?

Accepted Answer

$$x = 2$$

Question 11

A line passes through the point $$(0, -3)$$ and has a slope of $$\dfrac{1}{2}. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = \dfrac{1}{2}x - 3$$

Question 12

A water tank is being drained at a constant rate. The volume $$V (in $$gallons) after $$t$$ hours is given by $$V = 1200 - 75t. $$What is the volume after $$8$$ hours?

Accepted Answer

$$600$$

Question 13

Which of the following best describes the slope of the line $$y = -\dfrac{3}{4}x + 2$$?

Accepted Answer

The line decreases by $$3$$ units for every $$4$$ units increase in $$x.$$

Question 14

Find the equation of the line that passes through $$(2, 5)$$ and is parallel to the line $$y = 3x - 7.$$

Accepted Answer

$$y = 3x - 1$$

Question 15

A chemist is mixing a solution and models the temperature $$T (in $$degrees Celsius) as $$T = 25 + 0.5t$$, where $$t is $$the number of minutes since the start. What is the temperature after $$10$$ minutes?

Accepted Answer

$$30$$

Question 16

Which of the following is the correct domain for the function $$f(x) = \dfrac{5}{x^2$ - 9}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 17

A line passes through $$(4, 7)$$ and $$(8, 15). $$What is the slope of the line?

Accepted Answer

$$2$$

Question 18

If $$f(x) = x^2$ - 4x + 3$$, which of the following ordered pairs is a solution to the function equation?

Accepted Answer

$$(2, -1)$$

Question 19

A medical researcher models the number of patients in a study as $$N = 200 + 15t$$, where $$t is $$the number of weeks since the study began. What does the $$200$$ represent?

Accepted Answer

The initial number of patients at the start of the study.

Question 20

Write the equation of the line in point-slope form that passes through $$(5, -2)$$ with a slope of $$-4.$$

Accepted Answer

$$y + 2 = -4(x - 5)$$

College Algebra: Functions and Linear Equations – Study Guide for Quiz 1

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