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

Question 1

Solve the equation by factoring and using the zero product principle: $$x^2 - 3x - 40 = 0$

Accepted Answer

$$x = -8, x = 5$$

Question 2

Solve the equation by factoring and using the zero product principle: $$x^3$$ + $$2x^2 = 5x + 10$

Accepted Answer

$$x = -2, x = 2, x = 5$$

Question 3

Solve by using the square root property: $$2x^2 - 5 = -55$

Accepted Answer

$$x = \pm 5$$

Question 4

Solve the radical equation: $$\sqrt{2x + 13} = x + 7$$

Accepted Answer

Question 5

Evaluate the piecewise function $$f(x) = \begin{cases} 5, & x \leq 4 \ x + 4, & x \u003e 4 \end{cases} at$$ $$x = -4.$$

Accepted Answer

$$f(-4) = 5$$

Question 6

Given the points $$(5, 6)$$ and $$(-3, -9)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = 2$$

Question 7

Write the equation of a line in point-slope form with slope $$-4$$ passing through $$(-8, 6).$$

Accepted Answer

$$y - 6 = -4(x + 8)$$

Question 8

Find the domain of the function $$f(x) = \dfrac{2x}{x^2$ - 49}.$$

Accepted Answer

$$x 
eq 7, x 
eq -7$$

Question 9

Determine if the pair of functions $$f(x) = 8x + 3$$ and $$g(x) = \dfrac{x - 3}{8}$$ are inverses of each other.

Accepted Answer

Yes, they are inverses.

Question 10

Find the inverse of the function $$f(x) = \dfrac{3x - 2}{5}.$$

Accepted Answer

$$f^{-1}(x$$) = \dfrac{5x + 2}{3}$$

Question 11

Determine the vertex of the graph of $$f(x) = -4x^2$ + 4x + 2.$$

Accepted Answer

$$(0.5, 3)$$

Question 12

Use the Leading Coefficient Test to determine the end behavior of the graph of $$f(x) = 2x^3$ + 3x^2$ - x + 5.$$

Accepted Answer

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

Question 13

Find the $$x-$$intercepts and their multiplicity for $$f(x) = x^4$ - 81x^2$.

Accepted Answer

$$x = 0 ($$multiplicity 1), $$x = 9 ($$multiplicity 1), $$x = -9 ($$multiplicity 1)$$; 
$$Graph crosses the $$x-$$axis at all intercepts.

Question 14

Divide using long division: $$(x^2 + 7x + 10$$) \div (x + 2)$$.

Accepted Answer

$$x + 5$$

Question 15

Use the Rational Zero Theorem to find all possible rational zeros for $$f(x) = -x^4$ + 2x^3$ - 14x^2$ - 12x + 20.$$

Accepted Answer

$$\pm1, \pm2, \pm4, \pm5, \pm10, \pm20, \pm1/2, \pm2/1, \pm4/1, \pm5/1, \pm10/1, \pm20/1$$

Question 16

Solve the rational inequality and express the solution set in interval notation: $$\dfrac{x + 2}{x - 3} \geq 0.$$

Accepted Answer

$$(-\infty, -2] \cup (3, \infty)$$

Comprehensive Precalculus Study Guide – Step-by-Step Guidance

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