Question 1

Which of the following statements best describes an even function?

Accepted Answer

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

Question 2

A function $$f is $$said to be odd if:

Accepted Answer

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

Question 3

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

Accepted Answer

Odd

Question 4

Suppose a function $$f is $$defined on $$[-3, 3]$$ and its graph is symmetric with respect to the y-axis. Which property does $$f$$ have?

Accepted Answer

Even

Question 5

If a function $$f is $$increasing on the interval $$[1, 4]$$, which of the following must be true for any $$x_1$$, $$x_2 in$$ $$[1, 4]$$ with $$x_1$$ \u003c $$x_2$$?

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$

Question 6

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

Accepted Answer

$$f(x) \u003c f(2)$$ for all \ x$$ near 2$

Question 7

Which of the following is true about the absolute minimum of a function $$f on an $$interval $$I$$?

Accepted Answer

It is the lowest point on the entire domain of $$f$$

Question 8

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

Accepted Answer

Neither

Question 9

A function $$f is $$decreasing on the interval $$(-\infty, 0). $$Which of the following is true for $$x_1$$ \u003c $$x_2$$ \u003c 0$$?

Accepted Answer

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

Question 10

Suppose the graph of a function $$f$$ has a local minimum at $$x = -1$$ and a local maximum at $$x = 2. $$Which of the following statements is correct?

Accepted Answer

$$f(-1) is $$the lowest value in some interval around $$x = -1$$

Question 11

Which of the following real-world scenarios best illustrates a function with an absolute maximum?

Accepted Answer

The daily temperature reaches its highest point at noon.

Question 12

If $$f(x) is an $$even function and $$f(3) = 7$$, what is $$f(-3)$$?

Accepted Answer

$$7$$

Question 13

If $$f(x) is an $$odd function and $$f(5) = -2$$, what is $$f(-5)$$?

Accepted Answer

$$2$$

Question 14

A function $$f is $$constant on the interval $$[a, b] if$$:

Accepted Answer

$$f(x_1$) = f(x_2$)$$ for all $$x_1$$, $$x_2 in$$ $$[a, b]$$

Question 15

Which of the following equations represents an even function?

Accepted Answer

$$f(x) = x^4$ - 2x^2$ + 1$$

Question 16

A function $$f$$ has an absolute minimum at $$x = 0$$ and an absolute maximum at $$x = 5. $$Which of the following is true?

Accepted Answer

$$f(0) is $$the lowest value of $$f on $$its domain

Question 17

Suppose $$f(x) is $$defined on $$[-2, 2]$$ and is increasing on $$[-2, 0)$$ and decreasing on $$(0, 2]. $$What can you conclude about $$x = 0$$?

Accepted Answer

$$x = 0 is a $$local maximum

Question 18

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

Accepted Answer

It is symmetric with respect to the origin.

Question 19

If $$f(x) is an $$even function and $$f(0) = 5$$, what is $$f(-0)$$?

Accepted Answer

$$5$$

Properties of Functions: Even/Odd, Increasing/Decreasing, Maxima and Minima

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