Question 1

A ladder is leaning against a building. The base of the ladder is 3 ft from the building, and the ladder is 12 ft long. How tall is the building where the ladder touches it?

Accepted Answer

$$\sqrt{12^2$ - 3^2$} = 11.57 ft$$

Question 2

Given the function $$f(x) = x^2$ - 2$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

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

Accepted Answer

$$x = -2, x = \frac{1}{3}$$

Question 4

Find the equation of the circle with center $$(-6,4)$$ and radius $$3.$$

Accepted Answer

$$(x+6)^2$$ + $$(y-4)^2 = 9$

Question 5

Given $$f(x) = 3x^2$ + 5x$$, find $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$6x + 5 + 3h$$

Question 6

A $$\933$ investment is compounded quarterly at 5$$\%$$ annual interest for 4$ years. What is the future value?

Accepted Answer

$$933(1 + \frac{0.05}{4}$$)^{16}$$

Question 7

Find the inverse of $$f(x) = \sqrt{x-3} + 1.$$

Accepted Answer

Question 8

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

Accepted Answer

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

Question 9

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^5$ - 5x$$

Question 10

Given $$f(x) = x^3$ - 3x^2$ + 5x$$, list all possible rational roots.

Accepted Answer

$$\pm1, \pm5$$

Question 11

Find the domain of $$f(x) = \frac{6}{x-4}.$$

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 12

Solve the inequality $$-8x + 9 \u003c 6.$$

Accepted Answer

$$x \u003e \frac{3}{8}$$

Question 13

Given $$y = x^2$ - 2x - 8$$, find the vertex.

Accepted Answer

$$(1, -9)$$

Question 14

Find the equation of the line in slope-intercept form passing through $$(3,5)$$ and $$(4,9).$$

Accepted Answer

$$y = 4x - 7$$

Question 15

Expand $$\log_x y - 3 \log_x z$$ using logarithm properties.

Accepted Answer

$$\log_x \frac{y}{z^3$}$$

Question 16

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

Accepted Answer

$$x^2 - x$

Question 17

Find the solution to the system: $$x + 4y + z = 2$$, $$x - 3y - z = -24$$, $$x + y + z = -11.$$

Accepted Answer

$$(2,1,-3)$$

Question 18

Given $$f(x) = \frac{1}{x-3} + 4$$, find the $$y-$$intercept.

Accepted Answer

$$(0, \frac{1}{-3} + 4)$$

Question 19

Given $$P(t) = 386000e$$^{-0.036t}$$, how long will it take for the population to reach 60$$,000$$?

Accepted Answer

$$t = \frac{\ln(60,000/386,000)}{-0.036}$$

College Algebra Final Exam Review: Comprehensive Study Notes

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