Question 1

Suppose $$f(x) = 2x + 3$$ and $$g(x) = x^2$. What is the formula for the composite function f(g(x$$))$$?

Accepted Answer

$$2x^2 + 3$

Question 2

Given $$h(x) = \sqrt{3x - 1}$$, decompose $$h(x)$$ into $$f(g(x))$$ where $$f$$ and $$g$$ are simpler functions.

Accepted Answer

$$f(x) = \sqrt{x},\ g(x) = 3x - 1$$

Question 3

Which of the following functions is NOT invertible on its entire domain?

Accepted Answer

$$f(x) = x^2$

Question 4

If $$f(x) = 5x - 7$$, what is the formula for $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{5}$$

Question 5

Which statement about the graph of an inverse function is correct?

Accepted Answer

It is a reflection of the original function across the line $$y = x.$$

Question 6

Given $$f(x) = x^2$ with domain x$$ \geq 0$$, what is the range of f$$^{-1}$$(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 7

If $$N(t) is $$the number of people and $$P(t) is $$the amount of food at time $$t$$, which formula gives the per-capita food supply?

Accepted Answer

$$R(t) = \frac{P(t)}{N(t)}$$

Question 8

Which of the following is a power function?

Accepted Answer

$$f(x) = 7x$$^{-2}$$

Question 9

For the polynomial $$P(x) = x^4$ - 5x^2$ + 4$$, how many turning points can its graph have at most?

Accepted Answer

$$3$$

Question 10

If $$P(x) = (x - 2)^3$(x + 1)^2$, what happens at x = -1$?

Accepted Answer

The graph touches and turns around at $$x = -1.$$

Question 11

Which rational function has a horizontal asymptote at $$y = 0$$?

Accepted Answer

$$r(x) = \frac{2x}{x^2$ + 1}$$

Question 12

A rational function $$r(x) = \frac{(x - 2)(x + 3)}{(x - 2)(x - 5)}$$ has which of the following at $$x = 2$$?

Accepted Answer

A hole (removable discontinuity)

Question 13

If $$f(x) = x^3$ and g(x$$) = \sqrt{x}$$, what is the domain of f(g(x$$))$$?

Accepted Answer

$$[0, \infty)$$

Question 14

Which of the following best describes the end behavior of $$f(x) = -2x^5$ + 3x^2$ as x$$ 	o -\infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 15

Which of the following statements about the zeros of a polynomial is true?

Accepted Answer

A zero with even multiplicity causes the graph to touch and turn around at the $$x-$$axis.

Question 16

Given $$r(x) = \frac{2x^2$ + 1}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 17

If $$y is $$inversely proportional to $$x^3$$, which equation represents this relationship?

Accepted Answer

$$y = \frac{k}{x^3$}$$

Question 18

A city’s crime rate per person is modeled by $$R(t) = \frac{C(t)}{P(t)}$$, where $$C(t) is $$the number of crimes and $$P(t) is $$the population. If $$C(2020) = 500$$ and $$P(2020) = 10,000$$, what is $$R(2020)$$?

Accepted Answer

$$0.05$$

Compositions, Inverses, and Combinations of Functions; Polynomial and Rational Functions

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