Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - x + 5$$?

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

Question 1

Given the quadratic function $$f(x) = x^2$ + 8x^2$ + 11x - 29$$, use the Rational Root Theorem to determine which of the following could be a possible rational root.

Accepted Answer

$$\frac{1}{1}$$

Question 2

Suppose $$f(x) = 2x^3$ - 5x^2$ + 4x - 8. $$What is $$f(2)$$?

Accepted Answer

$$0$$

Question 3

Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - x + 5$$?

Accepted Answer

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

Question 4

A company models its profit $$P (in $$thousands of dollars) by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). How many units should be sold to maximize profit?

Accepted Answer

$$x = 4$$

Question 5

Given the function $$f(x) = \frac{2x+1}{x-3}$$, which value of $$x is $$NOT in the domain?

Accepted Answer

$$x = 3$$

Question 6

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 7

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x-2)(x-3)$$

Question 8

A rational function $$R(x)$$ has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0. $$Which of the following could be $$R(x)$$?

Accepted Answer

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

Question 9

Given $$f(x) = x^2$ - 6x + 8$$, find all real zeros.

Accepted Answer

$$x = 2, x = 4$$

Question 10

Suppose $$f(x) = 3x^2$ - 12x + 9. $$What is the minimum value of $$f(x)$$?

Accepted Answer

$$f(2) = -3$$

Question 11

A population of bacteria is modeled by $$P(t) = 500e$$^{0.2t}$$, where t$ is time in hours. What is the population after 5 hours?

Accepted Answer

$$500e^{1}$$

Question 12

Which of the following is the correct inverse of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 13

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

Accepted Answer

$$9$$

Question 14

A ball is thrown upward with an initial velocity of 32 ft/s from a height of 48 ft. Its height after $$t$$ seconds is $$h(t) = -16t^2$ + 32t + 48. $$When does the ball reach its maximum height?

Accepted Answer

$$t = 1 s$$

Question 15

Which of the following is the correct solution to $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6, x = -1$$

Question 16

Given $$f(x) = x^3$ - 3x^2$ + 2x$$, which of the following is a local minimum?

Accepted Answer

$$(2, -4)$$

Question 17

A chemical reaction is modeled by $$C(t) = 100 - 80e$$^{-0.5t}$$, where C$ is the concentration at time t$. What is the initial concentration?

Accepted Answer

$$C(0) = 20$$

Question 18

Which of the following is the correct solution set for $$x^2 - 9 = 0$?

Accepted Answer

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

Question 19

Suppose the graph of $$y = f(x) is $$shown below and passes through $$(0, 2)$$, $$(1, 4)$$, $$(2, 8)$$, and $$(3, 16). $$Which type of function best models this data?

Accepted Answer

Exponential

Question 20

A medical dosage is modeled by $$D(t) = 50e$$^{-0.1t}$$, where t$ is time in hours. How long until the dosage drops below 10 mg?

Accepted Answer

$$t \u003e 16.1$$ hours

College Algebra: Midterm Exam 3 – Sample Questions Study Guide

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