$$f(x_1$) = f(x_2$)$$ \text{ for all } $$x_1$$, $$x_2$$ \in I$

$$f(x_1$) \u003e f(x_2$)$$ \text{ for all } $$x_1$$ \u003c $$x_2 in$$ $$(a, b)$

$$f(b) \u003c f(x)$$ \text{ for } x \text{ near } b$

Question 1

Given the graph of $$y = f(x) in $$Image 1, on which interval is the function increasing?

Accepted Answer

$$(-\infty, -1)$$

Question 2

For the function $$f(x)$$ shown in Image 1, what is the relative maximum value?

Accepted Answer

$$2$$

Question 3

Using the graph in Image 1, at which $$x-$$value does $$f(x)$$ attain a relative minimum?

Accepted Answer

$$x = 3$$

Question 4

Based on the graph in Image 2, what is the interval where $$f(x) is $$decreasing?

Accepted Answer

$$(-5, -2)$$

Question 5

Which of the following best describes the symmetry of the function in Image 2?

Accepted Answer

The function is neither even nor odd.

Question 6

Given $$f(x) = x^2$ - 3x + 2$$, find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}.$$

Accepted Answer

$$2x + h - 3$$

Question 7

Consider the piecewise function $$f(x) = \begin{cases} 3, & x \leq -1 \ x-2, & x \u003e -1 \end{cases}. $$What is $$f(-2)$$?

Accepted Answer

$$3$$

Question 8

For the function $$f(x) = 3x + 7$$, what is $$f(x+h)$$?

Accepted Answer

$$3x + 3h + 7$$

Question 9

Given $$f(x) = \frac{1}{x}$$, what is the simplified form of the difference quotient $$\frac{f(x+h)-f(x)}{h}$$?

Accepted Answer

$$-\frac{1}{x(x+h)}$$

Question 10

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

Accepted Answer

It is an even function.

Question 11

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

Accepted Answer

$$f(x_1$) = f(x_2$)$$ 	ext{ for all } $$x_1$$, $$x_2$$ \in I$

Question 12

Suppose $$f(x) is $$decreasing on $$(a, b). $$Which of the following must be true?

Accepted Answer

$$f(x_1$) \u003e f(x_2$)$$ 	ext{ for all } $$x_1$$ \u003c $$x_2 in$$ $$(a, b)$

Question 13

Given the piecewise function $$f(x) = \begin{cases} 40, & 0 \leq x \leq 15 \ 40 + 0.60(x-15), & x \u003e 15 \end{cases}$$, what is $$f(50)$$?

Accepted Answer

$$61$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following is a correct interpretation of a relative minimum at $$x = b$$?

Accepted Answer

$$f(b) \u003c f(x)$$ 	ext{ for } x 	ext{ near } b$

Question 16

If a function $$f is $$even, which symmetry does its graph have?

Accepted Answer

Symmetry about the $$y-$$axis

Question 17

Given the graph in Image 2, what is the $$y-$$intercept of $$f(x)$$?

Accepted Answer

$$y = 2$$

Question 18

For the function $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

It is an odd function.

Question 19

Suppose $$f(x) is $$defined as $$f(x) = x - 2$$ for $$x \u003e -1. $$What is $$f(0)$$?

Accepted Answer

$$-2$$

Study Notes: More on Functions and Their Graphs

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