Question 1

Which of the following is the correct domain for the function $$f(x) = \sqrt{5 - 2x}$$?

Accepted Answer

$$(-\infty, 2.5]$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of time $$t (in $$years) by $$P(t) = 10e$$^{0.2t}$$. What is the profit after 5 years, rounded to the nearest thousand dollars?

Accepted Answer

$$10e^{1}$$ \approx 27$$

Question 3

Which of the following is the inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{3}$$

Question 4

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

Accepted Answer

$$f(g(2)) = (2 + 1)^2$ = 9$$

Question 5

Solve the equation $$2^{x} = 16$ for x$.

Accepted Answer

$$x = 4$$

Question 6

Which of the following is the sum of the infinite geometric series $$3 + 1.5 + 0.75 + \ldots$$?

Accepted Answer

$$6$$

Question 7

A satellite dish is shaped like a parabola. If its equation is $$y = 0.5(x - 2)^2$ + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 1)$$

Question 8

Which of the following is the correct expansion of $$(x + 2)^3$ using the binomial theorem?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 9

If $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 10

A Ferris wheel has a radius of 20 meters. What is the length of the arc subtended by a central angle of $$\frac{\pi}{3}$$ radians?

Accepted Answer

$$\frac{20\pi}{3}$$ meters

Question 11

Which of the following is the correct equation for a circle centered at $$(3, -2)$$ with radius $$5$$?

Accepted Answer

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

Question 12

Solve the system of equations using the augmented matrix method:

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

Accepted Answer

$$x = 2,\ y = 1$$

Question 13

Which of the following is the rectangular (algebraic) form of the complex number $$4	ext{cis}\left(\frac{\pi}{3}ight)$$?

Accepted Answer

$$2 + 2\sqrt{3}i$$

Question 14

Which of the following is the correct graph for $$y = -2\sin(x) + 1$$?

Accepted Answer

A sine wave with amplitude 2, reflected over the x-axis, shifted up by 1

Question 15

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$32$$

Question 16

A ball is thrown upward and its height (in meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 14t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 12.0$$ meters

Question 17

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}[2a_1 + (n-1)d]$$

Question 18

Which of the following is an identity for $$\sin(2x)$$?

Accepted Answer

$$2\sin(x)\cos(x)$$

Question 19

A population of bacteria triples every 4 hours. If the initial population is 200, what is the population after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Math 244 – Precalculus Syllabus and Course Overview (Southwestern College, Summer 2026)

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