Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function that can be written as $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$n is a $$non-negative integer and $$a_n 
eq 0$.

Question 2

Given the polynomial $$f(x) = 2x^3$ - 5x^2$ + 3x - 7$$, what is the degree of the polynomial?

Accepted Answer

3

Question 3

Which of the following is a possible rational root of the polynomial $$f(x) = 6x^3$ + 5x^2$ - 7x + 2$$ according to the Rational Root Theorem?

Accepted Answer

$$\pm1, \pm2$$

Question 4

If $$f(x) = x^4$ - 2x^3$ + x - 5$$, which of the following describes the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 5

A company models its profit $$P(x) in $$thousands of dollars by the quadratic function $$P(x) = -2x^2$ + 8x + 10$$, 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 $$18$$ thousand dollars at $$x = 2$$ thousand units.

Question 6

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

Accepted Answer

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

Question 7

Solve the equation $$2x^2 - 3x - 5 = 0$ for x$.

Accepted Answer

$$x = \frac{5}{2} or$$ $$x = -1$$

Question 8

Which of the following describes the graph of $$f(x) = (x - 1)^2$?

Accepted Answer

A parabola opening upwards with vertex at $$(1, 0).$$

Question 9

A projectile is launched from the ground and its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t. $$What is the maximum height reached by the projectile?

Accepted Answer

$$20.41$$ meters

Question 10

Which of the following is the correct solution set for the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 11

Given $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 12

If $$f(x) = x^2$ + 4x + 4$$, what is the vertex of the parabola?

Accepted Answer

$$(-2, 0)$$

Question 13

Which of the following is the sum and product of the roots of $$x^2 - 7x + 12 = 0$?

Accepted Answer

Sum: $$7$$, Product: $$12$$

Question 14

A population of bacteria is modeled by $$P(t) = 500(1.05)^t$$, where $$t is $$the number of hours. What is the population after $$4$$ hours?

Accepted Answer

$$608$$

Question 15

Which of the following is the correct solution to $$|2x - 5| = 7$$?

Accepted Answer

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

Question 16

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

$$x 
eq 3$$ and $$x 
eq -3$$

Question 17

If $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(2x + 1)^2$ - 4$$

Question 18

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

Question 19

A ball is thrown upward from a balcony 20 meters above the ground with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 20. $$After how many seconds does the ball hit the ground?

Accepted Answer

$$t \approx 3.7$$ seconds

College Algebra Study Guide: Polynomial, Rational, Exponential, and Logarithmic Functions (Sections 3.5–4.4)

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