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

Area increases for $0 < w < 1500$ and decreases for $1500 < w < 3000$.

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

$0 < w < 3000$

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 $0 < w < 1500$ and decreases for $1500 < w < 3000$.

Relations and Functions in Business Calculus

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