Q: For the function $$f(x)$$ shown in the graph, determine $$\lim_{x \to 1} f(x)$$ and $$f(1).$$

a. $$\lim_{x \to 1} f(x) = 2$$; b. $$f(1) = 2$$

Q: Given the graph of $$f(x)$$, determine $$\lim_{x \to 2} f(x)$$ and $$f(2).$$

a. $$\lim_{x \to 2} f(x) = 1$$; b. $$f(2) = 2$$

Q: For the polynomial $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, which of the following describes its end behavior?

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

Question 1

Given the graph of a function, identify the open intervals where the function is concave upward and concave downward, and find any inflection points.

Accepted Answer

Concave upward on $$(-\infty, -2)$$ and $$(1, \infty)$$; concave downward on $$(-2, 1)$$; inflection points at $$(-2, -4)$$ and $$(1, -1.5).$$

Question 2

For the function $$f(x)$$ shown in the graph, determine $$\lim_{x 	o 1} f(x)$$ and $$f(1).$$

Accepted Answer

a. $$\lim_{x 	o 1} f(x) = 2$$; b. $$f(1) = 2$$

Question 3

Given the graph of $$f(x)$$, determine $$\lim_{x 	o 2} f(x)$$ and $$f(2).$$

Accepted Answer

a. $$\lim_{x 	o 2} f(x) = 1$$; b. $$f(2) = 2$$

Question 4

Determine the type of function for $$f(x) = 6x^4$ - 5x + 8.$$

Accepted Answer

Non-linear Polynomial

Question 5

If a polynomial $$f(x)$$ has a zero at $$x = a$$ with multiplicity 2, what does the graph do at $$x = a$$?

Accepted Answer

Touches the x-axis and turns around

Question 6

Find the coordinates of the vertex for the parabola defined by $$f(x) = x^2$ - 8x + 8.$$

Accepted Answer

$$(4, -8)$$

Question 7

Use the Leading Coefficient Test to determine the end behavior of $$f(x) = -3x^5$ + 2x^4$ - 6x.$$

Accepted Answer

Rises to the left and falls to the right

Question 8

What are the critical points to be used in solving the inequality $$8/(x-1)(x+3) \u003e 0$$?

Accepted Answer

$$-3, 1$$

Question 9

Does the rational function $$f(x) = \frac{x^2$ + 4x + 2}{x^2$ - 9}$$ have a slant or oblique asymptote?

Accepted Answer

No slant or oblique asymptote

Question 10

Given $$f(x) = \frac{3x^2$ - 8x + 2}{x^2$ - 12}$$, find the vertical asymptotes.

Accepted Answer

$$x = \sqrt{12}, x = -\sqrt{12}$$

Question 11

Use the graph of the rational function $$f(x) to $$complete the statement: As $$x 	o -\infty$$, $$f(x) 	o$$

Accepted Answer

$$-\infty$$

Question 12

Find the zeros of the polynomial $$f(x) = x^3$ - x^2$ - 2x + 12.$$

Accepted Answer

$$x = -2, x = 2, x = 3$$

Question 13

A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 258 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Accepted Answer

$$10,082\ 	ext{ft}^2$$

Question 14

Determine whether the quadratic function $$f(x) = ax^2$ + bx + c$$ where $$a, b, c$$ are positive numbers has a minimum or maximum value.

Accepted Answer

Minimum

Question 15

Find the vertical asymptotes, if any, of the graph of the rational function $$h(x) = \frac{x^2$}{x^2$ - 16}.$$

Accepted Answer

$$x = 4, x = -4$$

Question 16

Given the table of values for $$f(x) as$$ $$x$$ approaches $$-7$$ from both sides, what is $$\lim_{x 	o -7} f(x)$$?

Accepted Answer

$$-14$$

Question 17

Find the horizontal asymptote, if any, of the graph of the rational function $$f(x) = \frac{-3x - 5}{5x - 7}.$$

Accepted Answer

$$y = -\frac{3}{5}$$

Question 18

Divide $$9x^3$$ - $$18x^2 + 17x - 3$ by 3x + 4$ using long division. What is the quotient?

Accepted Answer

$$3x^2 - 10x + 17$$ - \frac{9}{3x + 4}$$

Question 19

For the polynomial $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, which of the following describes its end behavior?

Accepted Answer

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

Precalculus Study Guide: Functions, Graphs, and Polynomial Analysis

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