Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

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

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 8x + 6$$, what are the coordinates of its vertex?

Accepted Answer

$$(2, -2)$$

Question 3

A company’s revenue is given by $$R(x) = -x^2$ + 30x$$ and its cost by $$C(x) = 5x + 100. $$What is the maximum profit, and at what quantity $$x$$ does it occur?

Accepted Answer

Maximum profit is $$225 at$$ $$x = 12.5$$

Question 4

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

$$y = x^2$

Question 5

If $$f(x) = x^2$ and g(x) = f(x-3) + 2$, which transformation has been applied to f(x$$)$$ to obtain g(x$$)$$?

Accepted Answer

Shift right by 3 units and up by 2 units

Question 6

Given the function $$f(x) = \sqrt{x-1} + 2$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 7

Suppose the profit function for a business is $$P(x) = -2x^2$ + 32x - 192. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Question 8

Which of the following is NOT a property of a quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

The graph is always a straight line.

Question 9

If $$f(x) is an $$even function, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = f(x)$$

Question 10

A rectangular lot is to be fenced on three sides with fencing and on one side with a brick wall. If $$100$$ meters of fencing is available for the other three sides, and the area is $$A = l(100 - l/2)$$, what value of $$l$$ maximizes the area?

Accepted Answer

$$l = 100$$

Question 11

Which of the following best describes the range of the function $$y = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 12

If $$f(x) = x^2$ and g(x) = -f(x$$)$$, what transformation has been applied to f(x$$)$$ to obtain g(x$$)$$?

Accepted Answer

Reflection across the x-axis

Question 13

Which of the following is the correct formula for the axis of symmetry of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$x = \frac{-b}{2a}$$

Question 14

Given the function $$f(x) = 2x^2$ - 3x + 1$$, find all $$x$$ such that $$f(x) = 0.$$

Accepted Answer

$$x = 1 or$$ $$x = \frac{1}{2}$$

Question 15

Which of the following statements about the range of $$f(x) = \frac{1}{x^2$ - 4} is $$correct?

Accepted Answer

$$(0, \infty)$$

Question 16

If the graph of $$y = f(x) is $$translated 4 units to the right, which equation represents the new graph?

Accepted Answer

$$y = f(x-4)$$

Question 17

Which of the following is an example of a function that is odd?

Accepted Answer

$$f(x) = x^3$

Question 18

Suppose $$f(x) = x^2$ - 4x + 3. $$What are the $$x-$$intercepts of the graph of $$f$$?

Accepted Answer

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

Business Calculus: Functions and Quadratic Functions – Properties, Graphs, and Applications

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