Q: Which of the following statements is true about an even function $$f(x)$$?

$$f(-x) = f(x)$$ \text{ for all } x \text{ in the domain}$

Q: A function $$f$$ has a local maximum at $$x = 2 if$$:

$$f(2) \u003e f(x)$$ \text{ for all } x \text{ near } 2$

Question 1

Given the function $$f(x) = \frac{x+3}{x+4}$$, what is the domain of $$f$$?

Accepted Answer

$$\{x \mid x 
eq -4\}$$

Question 2

Which of the following statements is true about an even function $$f(x)$$?

Accepted Answer

$$f(-x) = f(x)$$ 	ext{ for all } x 	ext{ in the domain}$

Question 3

A plane crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost per passenger is given by $$C(x) = 150 + \frac{30000}{x}$$, where $$x is $$the ground speed. What is the cost per passenger when the ground speed is 600 miles per hour?

Accepted Answer

$$200$$

Question 4

For the function $$f(x) = x^3$ - 5x$$, determine whether $$f is $$even, odd, or neither.

Accepted Answer

Odd

Question 5

Given the graph of a function $$f(x)$$, which of the following intervals describes where the function is increasing?

Accepted Answer

$$(-\infty, -2) \cup (2, 4)$$

Question 6

If $$f(x) is $$continuous on $$[a, b]$$, which theorem guarantees that $$f$$ attains both an absolute maximum and an absolute minimum on $$[a, b]$$?

Accepted Answer

Extreme Value Theorem

Question 7

Suppose $$f(x) is $$decreasing on the interval $$[1, 3]. $$Which of the following is true for any $$x_1$$, $$x_2 in$$ $$[1, 3]$$ with $$x_1$$ \u003c $$x_2$$?

Accepted Answer

$$f(x_1$) \u003e f(x_2$)$$

Question 8

A function $$f$$ has a local maximum at $$x = 2 if$$:

Accepted Answer

$$f(2) \u003e f(x)$$ 	ext{ for all } x 	ext{ near } 2$

Question 9

Given $$f(x) = x^2$ + 3$$, determine if $$f is $$even, odd, or neither.

Accepted Answer

Even

Question 10

For the function $$f(x) = \frac{x+3}{x+4}$$, what is the $$x-$$intercept?

Accepted Answer

$$x = -3$$

Question 11

Which of the following best describes the symmetry of an odd function?

Accepted Answer

Symmetric with respect to the origin

Question 12

If a function $$f is $$constant on an interval $$[a, b]$$, what can be said about $$f(x)$$ for $$x in$$ $$[a, b]$$?

Accepted Answer

$$f(x) is $$the same for all $$x in$$ $$[a, b]$$

Question 13

A function $$f is $$defined on $$[0, 4]$$ and has local maxima at $$x = 1$$ and $$x = 3. If$$ $$f(1) = 5$$ and $$f(3) = 7$$, what is the absolute maximum value of $$f on$$ $$[0, 4] if$$ $$f(0) = 2$$ and $$f(4) = 6$$?

Accepted Answer

$$7$$

Question 14

Which of the following intervals describes where the function $$f(x) is $$decreasing, given that $$f(x) is $$decreasing on $$(-\infty, -2)$$ and $$(2, 4)$$?

Accepted Answer

$$(-\infty, -2) \cup (2, 4)$$

Question 15

If $$f(x) is $$continuous on $$[a, b]$$ and $$f(a) = f(b)$$, which theorem guarantees that for every value $$k$$ between $$f(a)$$ and $$f(b)$$, there is some $$c in$$ $$[a, b]$$ such that $$f(c) = k$$?

Accepted Answer

Intermediate Value Theorem

Question 16

For the function $$f(x) = x^2$ - 4x + 3$$, what is the $$y-$$intercept?

Accepted Answer

$$3$$

Question 17

Suppose $$f(x) is $$increasing on $$(-\infty, 0)$$ and decreasing on $$(0, \infty). $$What type of critical point does $$x = 0$$ represent?

Accepted Answer

Local maximum

Question 18

A function $$f is $$defined on $$[a, b]$$ and is continuous. Which of the following statements is always true?

Accepted Answer

$$f$$ attains both an absolute maximum and an absolute minimum on $$[a, b]$$

Question 19

Given the function $$f(x) = x^2$ - 4x + 3$$, for what values of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

College Algebra Study Notes: Functions, Graphs, and Extrema

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