Question 1

Which of the following is the correct definition of the slope of a line passing through two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 2

Given the points $$(1,2)$$ and $$(4,8)$$, what is the equation of the line passing through them in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 3

If $$f(x) = x^2$, what is the value of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Question 4

Which of the following is the correct equation for a line with slope $$m$$ passing through point $$(a, b)$$?

Accepted Answer

$$y - b = m(x - a)$$

Question 5

A chemical reaction's temperature $$T (in$$ $$^\circC) $$increases linearly with time $$t (in $$minutes). If $$T = 20$$ when $$t = 0$$ and $$T = 50$$ when $$t = 15$$, what is the equation relating $$T$$ and $$t$$?

Accepted Answer

$$T = 2t + 20$$

Question 6

Which of the following statements is true about the graph of $$y = x^2$?

Accepted Answer

It is symmetric about the $$y-$$axis.

Question 7

A medical dosage $$D (in mg) is $$prescribed to increase by $$5 mg $$every day. If the initial dosage is $$20 mg$$, what will be the dosage after $$7$$ days?

Accepted Answer

$$D = 55 mg$$

Question 8

Which of the following is NOT a function?

Accepted Answer

A relation where some inputs have more than one output.

Question 9

If $$f(x) = 3x - 4$$, what is $$f(5)$$?

Accepted Answer

$$11$$

Question 10

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 0.20m + 30$$

Question 11

Which of the following is the correct solution to the equation $$2x + 5 = 17$$?

Accepted Answer

$$x = 6$$

Question 12

If $$g(x) = x^2$ - 3x + 2$$, what is $$g(4)$$?

Accepted Answer

$$6$$

Question 13

Which of the following best describes the solution set of $$x^2 = 9$?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 14

A line passes through $$(2, 5)$$ and has a slope of $$-3. $$What is its equation in point-slope form?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 15

Which of the following is the correct simplification of $$\frac{(x+2)^2$ - x^2$}{2}$$?

Accepted Answer

$$2x + 2$$

Question 16

A population of bacteria doubles every hour. If the initial population is $$100$$, what will be the population after $$3$$ hours?

Accepted Answer

$$800$$

Question 17

Which of the following is the correct formula for the difference quotient of $$f(x) = 5x + 7$$?

Accepted Answer

$$5$$

Question 18

If $$h(x) = x^2$ + 2x$$, what is $$h(x+1)$$?

Accepted Answer

$$(x+1)^2 + 2(x+1$$)$$

Question 19

A business's profit $$P is $$given by $$P = 4x - 10$$, where $$x is $$the number of units sold. How many units must be sold for the profit to be $$50$$?

Accepted Answer

$$x = 15$$

Question 20

Which of the following is the correct solution to $$3(x - 2) = 12$$?

Accepted Answer

$$x = 6$$

Fundamental Concepts in College Algebra: Functions, Slope, and Lines

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