Question 1

Given the function $$f(x) = \frac{2x^3$ - 6x}{x^2$ + 3}$$, evaluate $$f(-1)$$ and simplify your answer.

Accepted Answer

$$\frac{8}{2}$$

Question 2

Refer to the graph showing the percent of students in the College of Engineering at Stale University. Does the graph represent a function?

Accepted Answer

Yes, because each year corresponds to exactly one percentage.

Question 3

Using the same graph, what is $$f(1995)$$, the percentage of students enrolled in the College of Engineering in 1995?

Accepted Answer

About 18%

Question 4

If $$f(x) = 12\%$$, what year is represented by $$x$$ according to the graph?

Accepted Answer

1980

Question 5

Find and simplify the difference quotient for $$f(x) = 7x - 4.$$

Accepted Answer

$$7$$

Question 6

Write the equation of the line passing through $$(3, 5)$$ and $$(-5, 6) in $$point-slope form.

Accepted Answer

$$y - 5 = \frac{1}{8}(x - 3)$$

Question 7

A car's value depreciates from $$14,760 in 1991 to$$ $$4,440 in 1994. $$Let $$y be $$the value in year $$x$$, where $$x=0 is 1991. $$Write the linear equation modeling the value.

Accepted Answer

$$y = -4,106.67x + 14,760$$

Question 8

Find the average rate of change of $$f(x) = x^2$ from x = 2$ to x = 8$.

Accepted Answer

$$10$$

Question 9

Given $$f(x) = 2x^2$ + 2x - 2$$ and $$g(x) = 2x^2$ - 4x - 4$$, find $$(f \circ g)(-2).$$

Accepted Answer

$$54$$

Question 10

The function $$f(x) = 3x + 7 is $$one-to-one. Find the equation for $$f^{-1}(x$$)$$, the inverse function.

Accepted Answer

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

Question 11

Solve the equation $$8x^2 - 5x$$ = $$9x^2 - 36x + 4$ for x$.

Accepted Answer

$$x = 40, x = 1$$

Question 12

A ladder that is 10 feet long is 6 feet from the base of a wall. How far up the wall does the ladder reach?

Accepted Answer

$$8$$ feet

Question 13

You have 600 feet of fencing to enclose a rectangular plot that borders a river (no fence along the river). What is the largest area that can be enclosed?

Accepted Answer

$$90,000$$ square feet

Question 14

Solve the linear inequality $$24x - 20 \leq 4(5x - 6)$$ and write your answer in interval notation.

Accepted Answer

$$(-\infty, 0]$$

Question 15

Solve the compound inequality $$5 \leq 3x + 14 \u003c 29. $$Write your answer in interval notation.

Accepted Answer

$$[-3, 5)$$

Question 16

Find the domain of the rational function $$f(x) = \frac{x^3$ + 2x}{x^2$ - 16}.$$

Accepted Answer

$$x 
eq 4, x 
eq -4$$

Question 17

The intensity $$I of $$light varies inversely as the square of the distance $$D$$ from the source. If the intensity is $$2.5$$ foot-candles at $$28 ft$$, what is the intensity at $$40 ft$$?

Accepted Answer

$$1.225$$ foot-candles

Question 18

A city is growing at the rate of $$0.8\%$$ annually. If there were $$3,980,000$$ residents in 1995, how many are living in that city in 2000? Use $$y = 3,980,000(2.7$$)^{0.008t}$$, where t$ is years since 1995.

Accepted Answer

$$4,140,000$$

Question 19

Evaluate the expression $$\ln(e^2$) + 4\ln(e) - \ln(e).$$

Accepted Answer

$$5$$

Question 20

Find the sum of the infinite geometric series $$\frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \ldots.$$

Accepted Answer

$$1$$

College Algebra Final Exam Review – Graphs, Functions, and Applications

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