Question 1

Which of the following statements is TRUE about the end behavior of an odd-degree polynomial with a positive leading coefficient?

Accepted Answer

The graph starts negative and ends positive.

Question 2

Given the polynomial function $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following is TRUE about its graph?

Accepted Answer

It starts and ends positive if the leading coefficient is positive.

Question 3

A rational function is defined as $$f(x) = \frac{x^2$ - 4}{x^2$ - 1}. $$What are the vertical asymptotes of $$f(x)$$?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 4

Which of the following best describes the horizontal asymptote of the rational function $$f(x) = \frac{3x^2$ + 5}{2x^2$ - 7}$$?

Accepted Answer

$$y = 3/2$$

Question 5

A company models the number of products assembled per day by a new employee as $$N(t) = \frac{50t}{t+4}$$, where $$t is $$the number of days of training. What value does $$N(t)$$ approach as $$t$$ increases without bound?

Accepted Answer

$$N(t)$$ approaches 50

Question 6

Which of the following is a property shared by all polynomial functions?

Accepted Answer

Their graphs are always continuous and smooth.

Question 7

Suppose you are using a graphing calculator to perform a cubic regression on a data set. The resulting equation is $$y = 8.70x^3$ - 0.01x^2$ + 0.29x + 8.55$$ with $$R^2 = 0.995$. What does the R^2$ value indicate?

Accepted Answer

The model explains about 99.5% of the variation in the data.

Question 8

Which of the following rational functions has a horizontal asymptote at $$y = 0$$?

Accepted Answer

$$f(x) = \frac{2x^2$ + 1}{x^3$ - 4}$$

Question 9

If a rational function $$f(x) = \frac{n(x)}{d(x)}$$ has a common factor $$(x-2) in $$both numerator and denominator, what happens at $$x = 2$$?

Accepted Answer

There is a hole (removable discontinuity) at $$x = 2.$$

Question 10

Which of the following statements about polynomial regression is FALSE?

Accepted Answer

Polynomial regression always produces a perfect fit for any data set.

Question 11

A rational function $$f(x) = \frac{2x^2$ + 3x + 1}{x^2$ - 4} is $$given. What is the maximum number of vertical asymptotes this function can have?

Accepted Answer

2

Question 12

Which of the following is NOT a property of even-degree polynomial graphs with positive leading coefficients?

Accepted Answer

Their ends move in opposite directions.

Question 13

A polynomial function of degree 5 can change direction at most how many times?

Accepted Answer

4

Question 14

Which of the following best describes the domain of a rational function $$f(x) = \frac{x-3}{x-2}$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 15

Which of the following is TRUE about the range of an odd-degree polynomial function?

Accepted Answer

The range is all real numbers.

Question 16

A rational function $$f(x) = \frac{3(x^2$ + x - 2)}{2(x^2$ - 1)}$$ reduces to $$\frac{3(x+2)}{2(x+1)}$$ after canceling common factors. What is the horizontal asymptote?

Accepted Answer

$$y = 3/2$$

Question 17

Which of the following is the best description of a bounded function?

Accepted Answer

A function whose graph lies between two horizontal lines.

Question 18

Which of the following is the only type of polynomial function that is bounded?

Accepted Answer

Constant function

Question 19

A rational function has a numerator of degree 4 and a denominator of degree 2. What can you say about its horizontal asymptote?

Accepted Answer

It has no horizontal asymptote.

Polynomial and Rational Functions: Properties, Graphs, and Applications 1.4

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