Question 1

Which of the following best describes the Cartesian coordinate system?

Accepted Answer

A system where each point is represented by an ordered pair of numbers $$(x, y).$$

Question 2

Given the function $$y = x^2$ - 2x + 1$$, what is the $$y-$$value when $$x = -1$$?

Accepted Answer

$$y = 4$$

Question 3

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

Accepted Answer

$$x \geq 0$$

Question 4

A company manufactures notebooks. The cost function is $$C(x) = 2000 + 5x$$ and the revenue function is $$R(x) = 7x. $$What is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 7x - (2000 + 5x)$$

Question 5

Which of the following graphs represents the function $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 6

If $$f(x) = x^3$, which of the following statements is true about its domain?

Accepted Answer

The domain is all real numbers.

Question 7

Suppose the cost to produce $$x$$ units is $$C(x) = 2000 + 5x$$ and the revenue is $$R(x) = 7x. $$For what values of $$x$$ does the company break even?

Accepted Answer

$$x = 1000$$

Question 8

Which of the following is the correct range for the function $$f(x) = x^2$?

Accepted Answer

$$y \geq 0$$

Question 9

Given the function $$f(x) = \sqrt[3]{x}$$, which of the following is true?

Accepted Answer

The domain is all real numbers.

Question 10

Which of the following best describes the graph of $$f(x) = x$$?

Accepted Answer

A straight line passing through the origin with slope 1

Question 11

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

Accepted Answer

$$9$$

Question 12

Which of the following is the correct formula for the profit function if the cost is $$C(x) = 2000 + 5x$$ and the revenue is $$R(x) = 7x$$?

Accepted Answer

$$P(x) = 7x - (2000 + 5x)$$

Question 13

Which function has a domain of $$x \geq 0$$ and a range of $$y \geq 0$$?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 14

If the cost to produce $$x$$ units is $$C(x) = 2000 + 5x$$ and the revenue is $$R(x) = 7x$$, what is the profit when $$x = 1500$$?

Accepted Answer

$$P(1500) = 5500$$

Question 15

Which of the following is NOT an elementary function shown in the study materials?

Accepted Answer

$$f(x) = \sin(x)$$

Business Calculus Study Notes: Functions and Graphs

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