Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

A company’s revenue $$R (in $$dollars) from selling $$x$$ units is modeled by $$R(x) = 50x - 0.5x^2$. What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$1250 at$$ $$x = 50$$

Question 3

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 4

Solve the system of equations using matrices:

$$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 5

Which of the following is the correct solution to the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, what is the population after 12 hours? (Use the exponential model $$P(t) = P_0$ \cdot a$$^{t}$$)

Accepted Answer

$$5400$$

Question 7

Which of the following is the sum of the geometric series $$2 + 6 + 18 + 54$$?

Accepted Answer

$$80$$

Question 8

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

Accepted Answer

$$9$$

Question 9

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 25$

Question 10

Solve for $$x$$: $$\log_2$(x) + \log_2$(x-2) = 3$$

Accepted Answer

$$x = 4$$

Question 11

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

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

Question 12

A quadratic function models the height $$h (in $$meters) of a ball $$t$$ seconds after it is thrown: $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.9$$ meters

Question 13

Which of the following is the solution set for the rational equation $$\frac{2}{x} = x - 3$$?

Accepted Answer

$$x = 1, x = -2$$

Question 14

Which of the following is the sum of the first 5 terms of the arithmetic sequence where $$a_1 = 7$ and d = 3$?

Accepted Answer

$$45$$

Question 15

A radioactive substance decays according to $$A(t) = 100e$$^{-0.2t}$$. How much remains after 5 hours (rounded to the nearest whole number)?

Accepted Answer

$$37$$

Question 16

Which of the following is the correct solution to the inequality $$\frac{x+2}{x-1} \u003e 0$$?

Accepted Answer

$$(-2, 1) \cup (1, \infty)$$

Question 17

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

Accepted Answer

$$17$$

Question 18

Which of the following is the correct equation for the parabola with vertex at $$(1, -2)$$ and opening upwards?

Accepted Answer

$$y = a(x-1)^2$ - 2$$

Question 19

Which of the following is the correct formula for the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r$$?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

College Algebra (MATH 1314) Syllabus and Course Structure – Lone Star College

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