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 $$b in$$ $$I$$, $$a \u003c b$$ implies $$f(a) \u003c f(b)$$

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 $$a  f(b)$$

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

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