Question 1

Which of the following is the correct factorization of the trinomial $$7x^2 + 13x - 2$?

Accepted Answer

$$ (7x - 1)(x + 2) $$

Question 2

Given the function $$f(x) = -5x + 1$$, what is $$f(-3)$$?

Accepted Answer

$$ 16 $$

Question 3

A rectangular region is to be enclosed with 240 feet of fencing. What is the maximum area that can be enclosed?

Accepted Answer

$$ 3600 $$ square feet

Question 4

Solve the equation $$2x^2 = 26$ using the square root property.

Accepted Answer

$$ x = \pm \sqrt{13} $$

Question 5

What is the domain and range of the relation $$\{(6,7), (10,-8), (9,6), (9,2)\}$$?

Accepted Answer

Domain: $$\{6, 10, 9\}$$; Range: $$\{7, -8, 6, 2\}$$

Question 6

Given the equation $$10x - 12y - 120 = 0$$, what is the slope and y-intercept of its graph?

Accepted Answer

Slope: $$\frac{5}{6}$$; y-intercept: $$-10$$

Question 7

Find the zeros of the polynomial function $$f(x) = x^3$ + x^2$ - 20x.$$

Accepted Answer

$$ x = 0, x = -5, x = 4 $$

Question 8

What is the vertical asymptote of the rational function $$h(x) = \frac{x}{x(x+1)}$$?

Accepted Answer

$$ x = -1 $$

Question 9

The rabbit population in a forest area grows at a rate of 5% monthly. If there are 150 rabbits in September, how many rabbits should be expected by next September? Use $$y = 150(2.7$$)^{0.05t}$$, where t$ is the number of months.

Accepted Answer

$$ 272 $$ rabbits

Question 10

Write the equation $$3^{-3} = 1/27$ in its equivalent logarithmic form.

Accepted Answer

$$ \log_3$ 1/27 = -3 $$

Question 11

Expand the logarithmic expression $$\log_5$(25x)$$ using properties of logarithms.

Accepted Answer

$$ 2 + \log_5$ x $$

Question 12

Solve the equation $$4^{3x-7} = 16$ by expressing each side as a power of the same base and equating exponents.

Accepted Answer

$$ x = 3 $$

Question 13

The logistic growth function $$f(t) = \frac{720}{1 + 8.0e$$^{-0.13t}$$}$$ describes the population of butterflies $$t$$ months after introduction. How many butterflies were initially introduced?

Accepted Answer

$$ 80 $$ butterflies

Question 14

Solve the system of equations using the addition method: $$x - 4y = -15$$ and $$8x - 5y = 42. $$What is the solution?

Accepted Answer

$$ (9, 6) $$

Question 15

Write the first four terms of the sequence whose general term is $$a_n = 4n - 2.$$

Accepted Answer

$$ 2, 6, 10, 14 $$

Question 16

Find the sum $$\sum_{i=1}^{5} 2(2i-2).$$

Accepted Answer

$$ 20 $$

Question 17

Write the first five terms of the geometric sequence with $$a_1 = 3$ and r = -3$.

Accepted Answer

$$ 3, -9, 27, -81, 243 $$

Question 18

Find the sum of the first 11 terms of the geometric sequence $$2, 4, 8, 16, 32, \ldots.$$

Accepted Answer

$$ 4094 $$

Question 19

Solve the polynomial inequality $$x^2 - 8x + 12$$ \u003e 0$$ and express the solution set in interval notation.

Accepted Answer

$$ (-\infty, 2) \cup (6, \infty) $$

College Algebra Final Exam Review: Step-by-Step Study Guidance

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