Q: Suppose a function $f$ has a relative maximum at $x = c$. Which of the following must be true?

$f(c)$ is greater than $f(x)$ for all $x$ in some open interval containing $c$, except at $x = c$

Question 1

Given the function $f(x) = 2x - 4$, what is the zero of the function?

Accepted Answer

$x = 2$

Question 2

For the quadratic function $f(x) = x^2 - x - 2$, what are the zeros of the function?

Accepted Answer

$x = -1$ and $x = 2$

Question 3

A function $f$ is said to be increasing on an open interval $I$ if:

Accepted Answer

For all $a$ and $b$ in $I$, $a < b$ implies $f(a) < f(b)$

Question 4

Which of the following intervals describes where the function in the graph below is constant?

[Refer to the graph with points $(-1, -2)$ and $(3, -2)$ where the function is flat between these points]

Accepted Answer

$(-1, 3)$

Question 5

Suppose a function $f$ has a relative maximum at $x = c$. Which of the following must be true?

Accepted Answer

$f(c)$ is greater than $f(x)$ for all $x$ in some open interval containing $c$, except at $x = c$

Question 6

A community college has 30 ft of dividers to form two sides of a rectangular testing center in a corner. If $x$ is the length, what is the area $A(x)$ as a function of $x$?

Accepted Answer

$A(x) = 30x - x^2$

Question 7

For the area function $A(x) = 30x - x^2$, what value of $x$ gives the maximum area?

Accepted Answer

$x = 15$

Question 8

Given the function $f(x) = (x-2)^3$, what is the zero of the function?

Accepted Answer

$x = 2$

Question 9

If a function is decreasing on an interval $I$, which of the following is true?

Accepted Answer

For all $a < b$ in $I$, $f(a) > f(b)$

Question 10

A function $f$ is constant on an interval $I$ if:

Accepted Answer

For all $a$ and $b$ in $I$, $f(a) = f(b)$

Question 11

A real-world application requires maximizing the area of a rectangular region with a fixed perimeter. Which algebraic technique is most appropriate to find the maximum area?

Accepted Answer

Find the vertex of the quadratic area function

Question 12

Given the graph of a function, how do you determine the intervals where the function is increasing?

Accepted Answer

Look for intervals where the graph moves upward as $x$ increases

Question 13

If a function $f$ has a relative minimum at $x = c$, which statement is true?

Accepted Answer

$f(c)$ is less than $f(x)$ for all $x$ in some open interval containing $c$, except at $x = c$

Question 14

A function $f$ is defined on $(-\infty, \infty)$. If $f$ is constant on $(-1, 3)$, what does this mean about the values of $f(x)$ for $x$ in $(-1, 3)$?

Accepted Answer

$f(x)$ remains the same for all $x$ in $(-1, 3)$

Question 15

Suppose the area function for a rectangular region is $A(x) = 30x - x^2$. What is the maximum possible area?

Accepted Answer

$225$

Chapter 2: Analyzing Graphs of Functions – College Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards