Q: Which of the following statements about the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7 is $$correct?

$$\lim_{x \to \infty} f(x) = -\infty$$ and $$\lim_{x \to -\infty} f(x) = -\infty$$

Question 1

Which of the following best describes the transformation that occurs to the graph of $$y = x^2$ to produce the graph of y$$ = $$3(x-2)^2 + 4$?

Accepted Answer

Shift right 2 units, stretch vertically by 3, then shift up 4 units.

Question 2

Given the graph of a quadratic function with vertex at $$(1, -3)$$ and passing through the point $$(3, 5)$$, what is the equation of the function in vertex form?

Accepted Answer

$$y = 2(x-1)^2$ - 3$$

Question 3

A building is initially valued at $$50,000 and depreciates by 2$$,000 per year. What is the value of the building after 16 years?

Accepted Answer

$$18,000$$

Question 4

Which of the following graphs best represents a function with a strong positive linear association?

Accepted Answer

A scatterplot with points clustered along a line that rises from left to right.

Question 5

Given the function $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a real zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 6

If a rational function has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0$$, which of the following could be its equation?

Accepted Answer

$$f(x) = \frac{1}{x-2}$$

Question 7

A company models its monthly revenue $$R(x) (in $$dollars) as a function of the number of units $$x$$ sold by $$R(x) = -200x^2$ + 8000x. $$What is the maximum monthly revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$80,000 at$$ $$x = 20$$ units.

Question 8

Which of the following statements about the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7 is $$correct?

Accepted Answer

$$\lim_{x 	o \infty} f(x) = -\infty$$ and $$\lim_{x 	o -\infty} f(x) = -\infty$$

Question 9

Given the linear model $$y = 0.3975x + 18.016$$ for fuel economy (mpg) as a function of year $$x ($$years since 2000), what does the slope represent in this context?

Accepted Answer

The average increase in fuel economy per year.

Question 10

Which of the following is true about the correlation coefficient $$r$$ for a data set with a strong negative linear association?

Accepted Answer

$$r is $$close to $$-1$$

Question 11

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(h, k). $$Which formula gives the $$x-$$coordinate of the vertex?

Accepted Answer

$$h = -\frac{b}{2a}$$

Question 12

Which of the following best describes the graph of $$y = \frac{1}{x}$$?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0.$$

Question 13

If the average rate of change of a function $$f(x) is $$constant for all intervals, what type of function is $$f(x)$$?

Accepted Answer

A linear function

Question 14

Which of the following is a real-world example of a quadratic model?

Accepted Answer

The height of a ball thrown upward as a function of time.

Question 15

Given the rational function $$f(x) = \frac{x^2$ - 4}{x - 2}$$, what is the value of $$f(3)$$?

Accepted Answer

$$5$$

Question 16

Which of the following statements about polynomial functions is correct?

Accepted Answer

A polynomial of degree $$n$$ can have at most $$n$$ real zeros.

Question 17

If a function $$f(x) is $$even, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain.

Question 18

A scatterplot of data shows a strong positive linear association, but the residual plot shows a clear curve. What does this suggest about the appropriateness of a linear model?

Accepted Answer

A linear model is not appropriate; a nonlinear model may be better.

Question 19

Which of the following is the correct formula for the average rate of change of a function $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Polynomial and Rational Functions: Graphs, Models, and Applications

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