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

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

Question 1

Which of the following best describes the definition of a function?

Accepted Answer

A relation in which every input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$19$$

Question 3

Which of the following graphs represents a polynomial function?

Accepted Answer

A graph that is smooth and continuous.

Question 4

A company models its profit $$P(x) in $$thousands of dollars by the function $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$20$$ thousand dollars at $$x = 3$$ units.

Question 5

Which of the following is the correct domain of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$x \geq 4$$

Question 6

If $$f(x) = x^3$ - 2x$$ and $$g(x) = x + 5$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(2 + 5) = f(7) = 343 - 14 = 329$$

Question 7

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

Accepted Answer

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

Question 8

A medication's concentration in the bloodstream is modeled by $$C(t) = 5e$$^{-0.2t}$$, where t$ is time in hours. What is the concentration after 3$ hours?

Accepted Answer

$$C(3) = 5e$$^{-0.6}$$ \approx 2.74$$

Question 9

Which of the following is NOT a characteristic of polynomial functions?

Accepted Answer

They can have sharp corners.

Question 10

Given $$f(x) = x^2$ - 4x + 3$$, for which value(s) of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 11

A population of bacteria is modeled by $$P(t) = 1000(1.05)^t$$, where $$t is $$the number of hours. What is the population after $$8$$ hours?

Accepted Answer

$$P(8) = 1000(1.05)^8$ \approx 1477$$

Question 12

Which of the following is the inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 13

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 31.5$$ meters

Question 14

Which of the following describes the range of the function $$f(x) = x^2$?

Accepted Answer

All real numbers $$y \geq 0$$

Question 15

If $$f(x) = x^2$ and g(x) = 2x + 1$, what is f(g(3$$))$$?

Accepted Answer

$$f(g(3)) = f(7) = 49$$

Question 16

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 17

A car's value $$V (in $$dollars) after $$t$$ years is modeled by $$V(t) = 20000(0.85)^t. $$What is the value of the car after $$5$$ years?

Accepted Answer

$$V(5) = 20000(0.85)^5$ \approx 8860$$

Question 18

Which of the following is the correct solution to the equation $$2x^2 - 8x = 0$?

Accepted Answer

$$x = 0$$ and $$x = 4$$

Question 19

Which of the following is the correct vertex of the parabola $$y = x^2$ - 6x + 8$$?

Accepted Answer

$$(3, -1)$$

Study Guide: Functions, Graphs, and Polynomial Functions (College Algebra)

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