Question 1

Given the function $$f(x) = x^3$ - 2x^2$ + x - 5$$, which of the following is the correct domain and range of $$f(x)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$(-\infty, \infty)$$

Question 2

A ball is thrown vertically upward from the top of a building 800 feet tall with an initial velocity of 80 feet per second. The height $$h (in $$feet) of the ball after $$t$$ seconds is given by $$h(t) = -16t^2$ + 80t + 800. $$What is the maximum height reached by the ball?

Accepted Answer

$$900$$ feet

Question 3

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 2x$$

Question 4

Suppose a company’s profit function is $$P(x) = 52x - 1100$$, where $$x is $$the number of units sold. What is the break-even point?

Accepted Answer

$$x = 21.15$$

Question 5

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 3$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(2x + 3)^2$ - 4$$

Question 6

A radioactive substance decays according to the model $$A(t) = Ae$$^{-kt}$$, where A$ is the initial amount and k$ is a positive constant. If after 12 years, 80% of the original amount remains, what percent remains after 24 years?

Accepted Answer

$$64\%$$

Question 7

Which of the following is the correct solution to $$\log_2$(x) + \log_2$(x-1) = \log_2$(6)$$?

Accepted Answer

$$x = 3$$

Question 8

Given the rational function $$R(x) = \frac{2x^2$ + 3x - 2}{x^2$ - 4}$$, which of the following is the correct equation for the vertical asymptotes?

Accepted Answer

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

Question 9

A large group of students is asked to memorize a list of 60 Italian words. Suppose that the number of words remembered after $$t$$ hours is modeled by the function $$W(t) = 60(1 - e$$^{-0.5t}$$). $$What is the horizontal asymptote of this function?

Accepted Answer

$$y = 60$$

Question 10

Which of the following is the correct solution to $$6e^x = 9$$?

Accepted Answer

$$x = \ln(1.5)$$

Question 11

Given the polynomial $$f(x) = x^4$ - 4x^3$ + 2x^2$ - 8x + 8$$, which of the following is a possible rational zero?

Accepted Answer

$$x = 1$$

Question 12

If $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 3$$, what is $$f(g(x))$$?

Accepted Answer

$$(2x + 3)^2$ - 4$$

Question 13

Which of the following is the correct solution to $$x^2 = 4x + 5$?

Accepted Answer

$$x = -1$$ and $$x = 5$$

Question 14

A company charges a fixed cost of $$1500$$ with a variable cost per unit of $$22. $$The revenue function is $$R(x) = 52x. $$What is the profit function?

Accepted Answer

$$P(x) = 52x - 22x - 1500$$

Question 15

Which of the following is the correct solution to $$\log_3$(x^2) = 4$?

Accepted Answer

$$x = \pm 9$$

Question 16

Given the function $$f(x) = \frac{1}{x-2}$$, which of the following statements is true?

Accepted Answer

The function has a vertical asymptote at $$x = 2$$

Question 17

Which of the following is the correct solution to $$\frac{1}{x} + \frac{1}{x-1} = 5$$?

Accepted Answer

$$x = \frac{1}{5}$$ and $$x = \frac{1}{4}$$

Question 18

If $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 3$$, what is $$f(x) + g(x)$$?

Accepted Answer

$$x^2 + 2x - 1$

Question 19

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

College Algebra Final Exam Review: Comprehensive Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard