Question 1

A hospital tracks the temperature of a patient over time and graphs the data in the rectangular coordinate system. If the patient's temperature is plotted on the $$y-$$axis and time (in hours) on the $$x-$$axis, what does the slope of the line connecting two points represent?

Accepted Answer

The rate at which the patient's temperature changes per hour.

Question 2

Solve the linear equation for $$x$$: $$5x - 3 = 2x + 9$$

Accepted Answer

$$x = 4$$

Question 3

A chemical reaction is modeled by the equation $$\frac{2}{x} = 4. $$What is the value of $$x$$?

Accepted Answer

Question 4

A pharmaceutical company models the profit $$P as a $$function of the number of units sold $$n by$$ $$P(n) = 15n - 200. $$What is the break-even point (where profit is zero)?

Accepted Answer

$$n = \frac{200}{15}$$

Question 5

Multiply the complex numbers: $$(2 + 3i)(4 - 5i)$$

Accepted Answer

$$8 + 12i - 10i - 15i^2$ = 8 + 2i + 15 = 23 + 2i$$

Question 6

Solve the quadratic equation by factoring: $$x^2 - 5x + 6 = 0$

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 7

Express the interval $$[2, 5) in $$set-builder notation.

Accepted Answer

$$\{ x \mid 2 \leq x \u003c 5 \}$$

Question 8

Solve the linear inequality: $$3x - 7 \u003c 2x + 5$$

Accepted Answer

$$x \u003c 12$$

Question 9

Which of the following relations is a function?

Accepted Answer

$$\{ (1,2), (2,3), (3,4) \}$$

Question 10

Evaluate the function $$f(x) = 2x^2$ - 3x + 1 at$$ $$x = -2.$$

Accepted Answer

$$f(-2) = 15$$

Question 11

A company’s revenue function is $$R(x) = 5x + 20. On $$which interval is the function increasing?

Accepted Answer

On $$(-\infty, \infty)$$

Question 12

Find the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13).$$

Accepted Answer

$$m = 2$$

Question 13

Write the equation of the line in point-slope form that passes through $$(1, -2)$$ with slope $$m = 3.$$

Accepted Answer

$$y + 2 = 3(x - 1)$$

Question 14

Which of the following is the equation of a vertical line passing through $$(4, -7)$$?

Accepted Answer

$$x = 4$$

Question 15

Find the equation of the line perpendicular to $$y = 2x + 3$$ and passing through $$(0, 1).$$

Accepted Answer

$$y = -0.5x + 1$$

Question 16

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of f(g(x$$))$$?

Accepted Answer

$$[0, \infty)$$

Question 17

Determine if $$f(x) = 2x + 1$$ and $$g(x) = \frac{x - 1}{2}$$ are inverses of each other.

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 18

Find the distance between the points $$(1, 2)$$ and $$(4, 6).$$

Accepted Answer

$$5$$

Question 19

Write the standard form of the equation of a circle with center $$(3, -2)$$ and radius $$5.$$

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

College Algebra Study Guide: Step-by-Step Guidance for Key Topics

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