Question 1

For the following function, write the equation for the oblique asymptote: $$f(x) = \frac{x^2$ + 8x + 13}{x - 3}$$

Accepted Answer

$$y = x + 11$$

Question 2

Identify the domain and range of the following function: $$f(x) = \frac{14}{x}$$

Accepted Answer

Domain: $$(-\infty, 0) \cup (0, \infty)$$; Range: $$(-\infty, 0) \cup (0, \infty)$$

Question 3

Which of the following is the correct graph for $$f(x) = 6^x$$?

Accepted Answer

Graph passing through (0,1), (1,6), and approaching y=0 as $$x 	o -\infty$$

Question 4

Verify if the equation $$n^{7(\log_2 2^7)}$$ = $$n^7 is $$true. If not, make the necessary changes.

Accepted Answer

True

Question 5

For the given one-to-one function $$f(x) = x/2$$, find the inverse function $$f^{-1}(x$$)$$.

Accepted Answer

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

Question 6

Solve the following logarithmic equation for $$x$$: $$\log_3$(x + 9) = -2$$

Accepted Answer

Question 7

Use a calculator to approximate the value of $$e^{1.9} to $$four decimal places.

Accepted Answer

6.6858

Question 8

Determine a quadratic function $$f(x)$$ for the graph given below with vertex at (3, -9).

Accepted Answer

$$f(x) = x^2$ - 6x$$

Question 9

Solve the following equation by completing the square: $$y^2 - 8y - 3 = 0$

Accepted Answer

$$y = 4 \pm \sqrt{19}$$

Question 10

Determine the graph that the equation $$4x^2 + 64x$$ + $$4y^2 - 48y = 500$ represents.

Accepted Answer

Ellipse

Question 11

Write an equation for the line in slope-intercept form passing through $$(-2, 0)$$ and $$(4, 9).$$

Accepted Answer

$$y = 3x/2 + 3$$

Question 12

Solve the equation for $$x$$: $$11(4x + 1) + 3 = 25$$

Accepted Answer

$$x = 2/3$$

Question 13

By using the quadratic formula, solve the following equation: $$x^2 - 16x + 73 = 0$

Accepted Answer

$$x = 8 \pm 3i$$

Question 14

Identify if the given statement is correct or not: $$(7 + 3i) - (6 + 13i) = 11 + 16i$$

Accepted Answer

Incorrect statement; Correct statement should be $$(7 + 3i) - (6 + 13i) = 1 - 10i$$

Question 15

Enlist all values of $$x$$ that will make the given expression undefined: $$5/(x^2 - 7x + 6$$)$$

Accepted Answer

$$x = 1, 6$$

Question 16

Find the domain of the following square root function: $$\sqrt{10x - 5} - 3$$

Accepted Answer

$$(\frac{1}{2}, \infty)$$

Question 17

Perform multiplication in the given expression: $$b^2(5b - 3)(7b + 8$$)$$

Accepted Answer

$$35b^4$$ + $$19b^3$$ - $$24b^2$$

Question 18

Factor the following polynomial: $$14p^2 - 19pq$$ - $$3q^2$$

Accepted Answer

$$(7p + q)(2p - 3q)$$

Question 19

By factoring out and eliminating the common factors (if there are any) in the numerator and denominator, simplify the following rational expression: $$\frac{4(3y + 2)^3$ - (y + 5)(3y + 2)^2$}{(3y + 2)^3$}$$

Accepted Answer

$$\frac{(3y + 11)}{(3y + 2)}$$

Precalculus Study Guide: Key Concepts and Practice Problems

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