Question 1

Which of the following is the correct factorization of the quadratic expression $$x^2 - 5x + 6$?

Accepted Answer

$$ (x - 2)(x - 3) $$

Question 2

Given the quadratic equation $$2x^2 - 4x + 1 = 0$, what is the value of the discriminant, and how many real solutions does the equation have?

Accepted Answer

Discriminant is $$8$$, two real solutions

Question 3

Solve the absolute value equation $$|2x - 5| = 7.$$

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 4

Which of the following is the correct solution set for the inequality $$3x - 4 \u003c 2$$?

Accepted Answer

$$x \u003c 2$$

Question 5

Given the function $$f(x) = x^2$ - 4x + 7$$, evaluate $$f(-2).$$

Accepted Answer

$$f(-2) = 19$$

Question 6

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 2x-1 & x \geq 0 \end{cases}$$, what is $$f(3)$$?

Accepted Answer

$$5$$

Question 7

Given $$f(x) = 2x^2$ + 3x$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$4x + 2h + 3$$

Question 8

Determine whether the function $$f(x) = x^3$ is even, odd, or neither.

Accepted Answer

Odd

Question 9

What is the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 10

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 11

Solve the quadratic equation $$x^2 + 6x + 9 = 0$ using the square root property.

Accepted Answer

$$x = -3$$

Question 12

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

Accepted Answer

$$[0, \infty)$$

Question 13

Given the function $$f(x) = -x^2$ + 4x - 1$$, on which interval is the function increasing?

Accepted Answer

$$(-\infty, 2)$$

Question 14

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

Accepted Answer

$$10$$

Question 15

Which of the following is the $$y-$$intercept of the function $$f(x) = 5x - 7$$?

Accepted Answer

$$-7$$

Question 16

A ball is thrown upward from a height of $$2$$ meters with an initial velocity of $$8 m/s. $$Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 8t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$8.16$$ meters

Question 17

Which of the following relations is NOT a function?

Accepted Answer

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

Question 18

Given the function $$f(x) = x^2$ - 9$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 19

If $$f(x) = 2x + 1$$ and $$f(a) = 7$$, what is the value of $$a$$?

Accepted Answer

$$3$$

Key Concepts and Skills in College Algebra: Equations, Functions, and Graphs

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