Q: Which of the following statements correctly defines an even function?

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

Q: Suppose $$f(x)$$ has a local maximum at $$x = 2. $$Which of the following must be true?

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

Question 1

Which of the following statements correctly defines an even function?

Accepted Answer

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

Question 2

Given $$f(x) = x^3$ + 4x$$, determine whether $$f is $$even, odd, or neither.

Accepted Answer

Odd

Question 3

Which of the following graphs is symmetric with respect to the y-axis?

Accepted Answer

The graph of $$f(x) = x^2$

Question 4

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

Accepted Answer

For any $$x_1  f$$($$x_2$$)$$

Question 5

Suppose $$f(x)$$ has a local maximum at $$x = 2. $$Which of the following must be true?

Accepted Answer

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

Question 6

If a function $$f is $$continuous on $$[a, b]$$, what does the Extreme Value Theorem guarantee?

Accepted Answer

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

Question 7

Find the average rate of change of $$f(x) = x^2$ + 1$$ from $$x = 1 to$$ $$x = 2.$$

Accepted Answer

$$3$$

Question 8

Given $$g(x) = x^2$ - 3x + 2$$, what is the equation of the secant line through $$(1, g(1))$$ and $$(3, g(3))$$?

Accepted Answer

$$y = x - 1$$

Question 9

Which of the following is true about the function $$f(x) = 1 + |x|$$?

Accepted Answer

$$f is $$even

Question 10

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

Accepted Answer

For all $$x in$$ $$I$$, $$f(x) is $$equal

Question 11

Suppose $$f(x) is $$defined on $$[0, 5]$$ and $$f(3) = 6 is $$the largest value of $$f on $$this interval. What is the absolute maximum of $$f on$$ $$[0, 5]$$?

Accepted Answer

$$6$$

Question 12

If $$f(x) is $$increasing on $$[1, 4]$$ and decreasing on $$[4, 7]$$, what can you conclude about $$x = 4$$?

Accepted Answer

$$f$$ has a local maximum at $$x = 4$$

Question 13

Which of the following is the correct formula for the average rate of change of $$f$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\dfrac{f(b) - f(a)}{b - a}$$

Question 14

Given $$f(x) = x^3$ + 3$$, is $$f$$ even, odd, or neither?

Accepted Answer

Neither even nor odd

Question 15

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the average rate of change of height from $$t = 1 to$$ $$t = 3$$ seconds?

Accepted Answer

$$\dfrac{h(3) - h(1)}{3 - 1}$$

Question 16

If $$f(x) is $$odd, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = -f(x)$$

Question 17

Suppose a function $$f is $$continuous on $$[2, 6]$$ and $$f(2) = 5$$, $$f(4) = 1$$, $$f(6) = 3. $$What is the absolute minimum value of $$f on$$ $$[2, 6]$$?

Accepted Answer

$$1$$

Question 18

Which of the following best describes the symmetry of the graph of $$f(x) = x^4$ - x^2$?

Accepted Answer

Symmetric with respect to the y-axis

Properties of Functions: Even/Odd, Increasing/Decreasing, Extrema, and Average Rate of Change

Guida di studio - Domande di pratica

Study guide - Flashcard