Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 2

Given the relation $$x^2$$ + $$y^2 = 4$, does this relation represent a function from x$ to y$?

Accepted Answer

No, because for some $$x$$ there are two possible $$y$$ values.

Question 3

For the function $$f(x) = \dfrac{1}{x^2$ - 4}$$, which of the following values is NOT in the domain?

Accepted Answer

$$x = 2$$

Question 4

Which of the following statements about the vertical line test is TRUE?

Accepted Answer

A graph passes the vertical line test if every vertical line intersects the graph at most once.

Question 5

Let $$f(x) = x^2$. Which of the following is TRUE about f(x$$)$$?

Accepted Answer

$$f(x) is an $$even function.

Question 6

Suppose $$f(x) = x^3$. What is the symmetry of the graph of f(x$$)$$?

Accepted Answer

Symmetric with respect to the origin.

Question 7

Given $$f(x) = 3x - 2x^2$, find and simplify the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$.

Accepted Answer

$$3 - 4x - 2h$$

Question 8

For the function $$g(x) = \dfrac{\sqrt{x-1}}{x^2$ - 4}$$, what is the domain?

Accepted Answer

$$x \geq 1$$ and $$x 
eq 2$$

Question 9

A car rental company charges a fixed $$44 drop-off fee plus 54 $$per day. Which of the following best represents the cost $$C(x) of $$renting the car for $$x$$ days?

Accepted Answer

$$C(x) = 44 + 54x$$

Question 10

Is the function $$C(x) = 44 + 54x$$ linear?

Accepted Answer

Yes, because it can be written in the form $$y = mx + b.$$

Question 11

Given the area of a field as $$A(w) = w(3000 - w)$$, what is the domain of $$A(w) if$$ $$w is $$the width in meters?

Accepted Answer

$$0 \u003c w \u003c 3000$$

Question 12

For the function $$f(x) = 2x + 1$$, determine whether it is even, odd, or neither.

Accepted Answer

Neither even nor odd

Question 13

If $$f(x) is an $$even function and $$g(x) is an $$odd function, what is the parity of $$f(x) + g(x)$$?

Accepted Answer

Neither even nor odd

Question 14

Suppose $$f(x) = x^2$ - 1. $$What is the range of $$f(x)$$?

Accepted Answer

$$[-1, \infty)$$

Question 15

Which of the following best describes the dependent variable in the function $$C(x) = 44 + 54x$$?

Accepted Answer

The cost of renting the car

Question 16

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

Accepted Answer

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

Question 17

Given $$f(x) = x^2$ and g(x$$) = $$x^3$$, what is the parity of $$f(x)g(x)$$?

Accepted Answer

Odd

Question 18

For the function $$A(w) = w(3000 - w)$$, what does the graph tell you about how the area varies with width?

Accepted Answer

Area increases for $$0 \u003c w \u003c 1500$$ and decreases for $$1500 \u003c w \u003c 3000.$$

Relations and Functions in Business Calculus

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