Q: Given $$f(x) = x + 2$$ and $$g(x) = 3x - 1$$, what is $$(f \circ g)(2)$$?

$$f(g(2)) = f(3 \times 2 - 1) = f(5) = 5 + 2 = 7$$

Q: A company’s profit $$P (in $$dollars) is modeled by $$P(x) = -5x^2$ + 200x - 1000$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units must be sold to achieve it?

Maximum profit is $$P(20) = -5(20)^2$ + 200 \times 20 - 1000 = 1000$$ dollars at $$x = 20$$ units

Q: If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f + g)(-3$$)$$?

$$f(-3) + g(-3) = (2 \times -3 + 1) + ((-3)^2$) = (-6 + 1) + 9 = -5 + 9 = 4$$

Question 1

Given the points $$A(2, -3)$$ and $$B(-4, 5)$$, what is the distance between $$A$$ and $$B$$?

Accepted Answer

$$\sqrt{(2 + 4)^2$ + (-3 - 5)^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 2

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4), (1,5)\}$$

Question 3

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15$

Question 4

Given $$f(x) = x + 2$$ and $$g(x) = 3x - 1$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(3 	imes 2 - 1) = f(5) = 5 + 2 = 7$$

Question 5

Which of the following best describes the graph of $$y = -|x - 3| + 2$$?

Accepted Answer

A downward-opening V-shape with vertex at $$(3, 2)$$

Question 6

What is the equation of the line passing through the points $$(1, 4)$$ and $$(3, 10) in $$point-slope form?

Accepted Answer

$$y - 4 = 3(x - 1)$$

Question 7

A company’s profit $$P (in $$dollars) is modeled by $$P(x) = -5x^2$ + 200x - 1000$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $$P(20) = -5(20)^2$ + 200 	imes 20 - 1000 = 1000$$ dollars at $$x = 20$$ units

Question 8

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ - 4$$

Question 9

Given $$f(x) = \sqrt{x - 1}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 10

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f + g)(-3$$)$$?

Accepted Answer

$$f(-3) + g(-3) = (2 	imes -3 + 1) + ((-3)^2$) = (-6 + 1) + 9 = -5 + 9 = 4$$

Question 11

Which transformation maps the graph of $$y = x^2$ to y = -2(x$$ - $$1)^2 + 3$?

Accepted Answer

Shift right 1, stretch vertically by 2, reflect over $$x-$$axis, shift up 3

Question 12

A piecewise function is defined as $$f(x) = \begin{cases} x + 2 & 	ext{if } x \u003c 0 \ x^2$ & 	ext{if } x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

$$(-3 + 2) + (2^2$) = (-1) + 4 = 3$$

Question 13

Which of the following best describes the graph of $$y = \sqrt{x + 4}$$?

Accepted Answer

Starts at $$x = -4$$ and increases to the right

Question 14

Given the linear equation $$3x - 4y = 12$$, what is the $$y-$$intercept?

Accepted Answer

$$y = -3$$

Question 15

Which of the following statements is true about the function $$f(x) = x^3$?

Accepted Answer

It is an odd function and its graph is increasing everywhere.

Question 16

A medical researcher models the temperature $$T (in$$ $$^\circC) of a $$patient after taking medication as $$T(t) = -0.5t^2$ + 2t + 37$$, where $$t is $$hours after taking the medication. What is the maximum temperature and when does it occur?

Accepted Answer

Maximum temperature is $$T(2) = -0.5(2)^2$ + 2 	imes 2 + 37 = -2 + 4 + 37 = 39 at$$ $$t = 2$$ hours

Question 17

Which of the following is the standard form of the equation of a line with slope $$m = -2$$ and $$y-$$intercept $$b = 5$$?

Accepted Answer

$$2x + y = 5$$

Question 18

If $$f(x) = |x|$$ and $$g(x) = x - 3$$, what is $$(f \circ g)(5)$$?

Accepted Answer

$$f(g(5)) = f(5 - 3) = f(2) = |2| = 2$$

Question 19

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(2, -3). $$Which of the following could be its equation?

Accepted Answer

$$f(x) = (x - 2)^2$ - 3$$

College Algebra Study Guide: Graphs and Functions, Linear and Quadratic Functions

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