Question 1

Solve for $$x in $$the equation $$2x^2 - 3x + 1 = 0$.

Accepted Answer

$$x = 1,\ x = \frac{1}{2}$$

Question 2

Which of the following is the equation of the circle with center $$(4, 4)$$ and radius $$3$$?

Accepted Answer

$$(x - 4)^2$ + (y - 4)^2$ = 9$$

Question 3

Find the vertex of the parabola $$f(x) = 2(x - 1)^2$ + 3.$$

Accepted Answer

$$(1, 3)$$

Question 4

Which of the following is the solution to $$\log_2$(x - 1) + 2\log_2$(x) = 3$$?

Accepted Answer

$$x = 4$$

Question 5

A population grows according to $$P(t) = 10,000e$$^{0.07t}$$. How many years will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.07}$$

Question 6

Which of the following is the equation of the line parallel to $$y = 2x - 5$$ and passing through $$(4, 6)$$?

Accepted Answer

$$y = 2x - 2$$

Question 7

Given $$f(x) = x^3$ - 3$$ and $$g(x) = x - 2$$, find $$(f \circ g)(x).$$

Accepted Answer

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

Question 8

Find the inverse of the function $$f(x) = 2x + 1.$$

Accepted Answer

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

Question 9

Solve the system of equations: $$\begin{cases} 2x + y = 4 \ x - y = 1 \end{cases}.$$

Accepted Answer

$$x = 1.67,\ y = 0.67$$

Question 10

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

Accepted Answer

$$x 
eq 3,\ x 
eq -3$$

Question 11

If $$\log_3$(x) = 4$$, what is the value of $$x$$?

Accepted Answer

$$x = 81$$

Question 12

Find the $$y-$$intercept of the function $$f(x) = x^2$ - 4x + 5.$$

Accepted Answer

$$y = 5$$

Question 13

Which of the following is the solution to $$|2x - 3| \u003c 1$$?

Accepted Answer

$$1 \u003c x \u003c 2$$

Question 14

A bank offers an interest rate of $$5\%$$ compounded quarterly. What is the effective annual rate?

Accepted Answer

$$5.09\%$$

Question 15

Which of the following is the sum $$\sum_{k=1}^4 (k^2$ - 2)$$?

Accepted Answer

$$24$$

Question 16

Given $$f(x) = 2x^2$ - 3x^2$ - 5x + 6$$, factor $$f(x)$$ into linear factors.

Accepted Answer

$$-(x - 6)(x - 1)$$

Question 17

Which of the following is the simplified form of $$\frac{1}{2}\log_a x + 4\log_a y - 3\log_a z as a $$single logarithm?

Accepted Answer

$$\log_a \left( \frac{\sqrt{x} y^4$}{z^3$} \right)$$

Question 18

If $$f(x) = \frac{2x}{x - 3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 19

Suppose two cars start 120 km apart and drive toward each other at 60 km/h and 40 km/h. How long until they meet?

Accepted Answer

$$2$$ hours

Question 20

Which of the following is the solution to $$2x^2 + 3x - 2 = 0$?

Accepted Answer

$$x = -2,\ x = \frac{1}{2}$$

College Algebra Final Exam Review: Comprehensive Study Notes

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