Question 1

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

Accepted Answer

$$10$$

Question 2

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(0,1), (1,2), (2,3)\}$$

Question 3

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

Accepted Answer

$$19$$

Question 4

Which of the following equations is in point-slope form for a line with slope $$m = -3$$ passing through $$(2, 5)$$?

Accepted Answer

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

Question 5

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

Accepted Answer

$$11$$

Question 6

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

Accepted Answer

Shifted right 3 units and up 2 units

Question 7

What is the vertex of the quadratic function $$f(x) = -2(x + 1)^2$ + 5$$?

Accepted Answer

$$(-1, 5)$$

Question 8

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 9

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -4x^2$ + 32x - 60$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$68 at$$ $$x = 4$$

Question 10

Which of the following is the domain of $$f(x) = \sqrt{x - 5}$$?

Accepted Answer

$$x \geq 5$$

Question 11

Given the function $$f(x) = \frac{2x}{x-1}$$, which value is NOT in the domain?

Accepted Answer

$$x = 1$$

Question 12

Which of the following describes the transformation from $$y = x^2$ to y = -3(x$$ - $$2)^2 + 4$?

Accepted Answer

Vertical stretch by 3, reflection over x-axis, right 2 units, up 4 units

Question 13

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

Accepted Answer

$$15$$

Question 14

Which of the following is the equation of a horizontal line passing through $$(4, -2)$$?

Accepted Answer

$$y = -2$$

Question 15

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$, what is $$f(-3) + f(2)$$?

Accepted Answer

$$7$$

Question 16

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

Accepted Answer

Starts at $$(0,0)$$ and increases slowly to the right

Question 17

If $$f(x) is an $$odd function and $$f(3) = 7$$, what is $$f(-3)$$?

Accepted Answer

$$-7$$

Question 18

A line passes through $$(1, 2)$$ and $$(5, 10). $$What is its equation in slope-intercept form?

Accepted Answer

Question 19

Which of the following best describes the range of $$f(x) = x^2$ - 4$$?

Accepted Answer

$$y \geq -4$$

College Algebra Study Notes: Graphs, Functions, and Linear & Quadratic Functions

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