Q: Find the inverse of the function $$f(x) = 3x - 7.$$

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

Q: Perform the long division and find the quotient for $$\\frac{x^3$ - 5x^2$ + 12x + 4}{x - 2}.$$

$$x^2 - 3x + 6$$ + \\frac{16}{x - 2}$$

Q: Find the accumulated value of an investment of $$8,000$$ for $$5$$ years at an interest rate of $$6.25\\%$$ compounded monthly. Use $$A = P(1 + \\frac{r}{n}$$)^{nt}$$.

$$A = 8,000(1 + \\frac{0.0625}{12}$$)^{60}$$

Q: Given $$f(x) = \\frac{4x}{x - 5}$$, find the inverse $$f^{-1}(x$$)$$.

$$f^{-1}(x$$) = \\frac{5x}{x - 4}$$

Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + x^3$ - 4$$?

As $$x \\to \\infty$$, $$f(x) \\to -\\infty$$; as $$x \\to -\\infty$$, $$f(x) \\to \\infty$$

Question 1

Given $$f(x) = x^2$ + 2x$$ and $$g(x) = x - 5$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(x - 5)^2$ + 2(x - 5)$$

Question 2

Find the inverse of the function $$f(x) = 3x - 7.$$

Accepted Answer

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

Question 3

A company models its revenue per day by $$R(x) = -x^2$ + 40x - 500. $$How many calculators should be sold each day to maximize revenue?

Accepted Answer

$$x = 20$$

Question 4

Given the polynomial $$f(x) = -3x^4$ + 2x^3$(x - 5)$$, what is the degree of the polynomial?

Accepted Answer

$$5$$

Question 5

Perform the long division and find the quotient for $$\frac{x^3$ - 5x^2$ + 12x + 4}{x - 2}.$$

Accepted Answer

$$x^2 - 3x + 6$$ + \frac{16}{x - 2}$$

Question 6

Find the domain of the function $$f(x) = \sqrt{11 - x}.$$

Accepted Answer

$$x \leq 11$$

Question 7

Solve the rational inequality $$\frac{x - 3}{x + 1} \u003e 0.$$

Accepted Answer

$$x \u003e 3 or$$ $$x \u003c -1$$

Question 8

The intensity $$I of a $$light source varies inversely as the square of the distance $$d. If $$the intensity is 12 units at 10 feet, what is the intensity at 5 feet?

Accepted Answer

$$I = 48$$

Question 9

Find the accumulated value of an investment of $$8,000$$ for $$5$$ years at an interest rate of $$6.25\%$$ compounded monthly. Use $$A = P(1 + \frac{r}{n}$$)^{nt}$$.

Accepted Answer

$$A = 8,000(1 + \frac{0.0625}{12}$$)^{60}$$

Question 10

Rewrite the exponential equation $$7^x = y in $$logarithmic form.

Accepted Answer

$$\log_7$ y = x$$

Question 11

Given $$f(x) = \frac{4x}{x - 5}$$, find the inverse $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{5x}{x - 4}$$

Question 12

If the height (in feet) of a bottle rocket is given by $$h(t) = -16t^2$ + 80t + 3$$, at what time does the rocket reach its maximum height?

Accepted Answer

$$t = 2.5$$

Question 13

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + x^3$ - 4$$?

Accepted Answer

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 14

Find the domain of the function $$f(x) = \frac{2x + 7}{x^2$ - 5}.$$

Accepted Answer

$$x \neq \pm \sqrt{5}$$

Question 15

Solve the inequality $$(2x - 10)(x + 7) \leq 0.$$

Accepted Answer

$$-7 \leq x \leq 5$$

Question 16

Change the logarithmic form $$\log_a x = 3 to $$exponential form.

Accepted Answer

$$x = a^3$

Question 17

If the volume of water flowing in a pipe varies directly as the pressure $$P$$, and the volume is $$10$$ liters when the pressure is $$8$$ units, what is the volume when the pressure is $$10$$ units?

Accepted Answer

$$12.5$$ liters

Question 18

Rewrite $$x^4 = 12$ in logarithmic form.

Accepted Answer

$$\log_{x} 12 = 4$$

Question 19

Given $$f(x) = 2x^2$ - 5x + 4$$, identify the vertex of the quadratic function.

Accepted Answer

$$(1.25, 0.375)$$

Precalculus Study Guide: Functions, Polynomials, Quadratics, Rational Expressions, Variation, Exponential and Logarithmic Forms

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