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

Question 1

Which of the following is the correct equation for a line passing through the points $$(2, 3)$$ and $$(4, 7)$$?

Accepted Answer

$$y = 2x - 1$$

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 3

Which of the following best describes the graph of $$y = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 4

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

Accepted Answer

$$9$$

Question 5

Which of the following intervals represents the domain of $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 6

A business’s profit function is $$P(x) = -2x^2$ + 8x + 10. $$What is the maximum profit, and at what value of $$x$$ does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 7

Which of the following is the correct inverse of the function $$f(x) = 3x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{3}$$

Question 8

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

Accepted Answer

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

Question 9

Which of the following is the correct equation for a circle centered at the origin with radius $$5$$?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 10

If $$f(x) = \frac{2x+1}{x-3}$$, what is the vertical asymptote?

Accepted Answer

$$x = 3$$

Question 11

Which of the following is the correct solution to the system: $$2x + y = 5$$ and $$x - y = 1$$?

Accepted Answer

$$(2, 1)$$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$$36$$

Question 14

Which of the following is the correct domain for $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 15

A company’s cost function is $$C(x) = 5x + 200. $$What is the fixed cost?

Accepted Answer

$$200$$

Question 16

Which of the following is the correct solution for $$x in$$ $$\ln(x) = 2$$?

Accepted Answer

$$x = e^2$

Question 17

Which of the following is the correct equation for a parabola opening upwards with vertex at $$(0,0)$$?

Accepted Answer

$$y = x^2$

Question 18

If $$f(x) = 2x^2$ - 8x + 6$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-2$$

Question 19

Which of the following is the correct horizontal asymptote for $$f(x) = \frac{3x^2$ + 2}{x^2$ - 1}$$?

Accepted Answer

$$y = 3$$

Question 20

Which of the following is the correct solution to $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln(7)$$

Business Calculus: Functions, Graphs, and Models – Comprehensive Study Notes

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