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

$$\lim_{x \to 1} f(x) = 2$$, $$f(1) = 1$$

Q: Given the graph, what is $$\lim_{x \to 2} f(x)$$ and $$f(2)$$?

$$\lim_{x \to 2} f(x) = 1$$, $$f(2) = 2$$

Question 1

Given the function $$f(x)$$ shown in the graph, identify the open intervals where the function is concave upward and concave downward. Also, find the inflection points.

Accepted Answer

Concave upward on $$(-\infty, -2)$$ and $$(1, \infty)$$; concave downward on $$(-2, 1)$$; inflection points at $$(-2, -4)$$ and $$(1, -5).$$

Question 2

For the function shown in the graph, what is $$\lim_{x 	o 1} f(x)$$ and $$f(1)$$?

Accepted Answer

$$\lim_{x 	o 1} f(x) = 2$$, $$f(1) = 1$$

Question 3

Given the graph, what is $$\lim_{x 	o 2} f(x)$$ and $$f(2)$$?

Accepted Answer

$$\lim_{x 	o 2} f(x) = 1$$, $$f(2) = 2$$

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

Falls 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 the rational function $$f(x) = \frac{2x^2$ - 5x + 2}{x^2$ - 9}$$, which of the following describes its asymptotes?

Accepted Answer

Vertical asymptotes at $$x = \pm 3$$, no horizontal asymptote

Question 11

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

Accepted Answer

$$-\infty$$

Question 12

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

Accepted Answer

$$x = 1, x = -1, x = 3$$

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

5014 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

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

Accepted Answer

$$y = -1$$

Question 17

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

Limit is $$-14$$

Question 18

Divide using long division: $$\frac{9x^3$ - 18x^2$ + 17x - 3}{3x + 4}.$$

Accepted Answer

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

Question 19

A chemical reaction rate $$R(t) is $$modeled by a rational function $$R(t) = \frac{2t^2$ + 5t + 3}{t^2$ - 4}. $$What is the horizontal asymptote of $$R(t)$$?

Accepted Answer

$$y = 2$$

Precalculus Study Guide: Functions, Polynomials, and Rational Functions

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