Algebra 21.2 Notes

1.2 Characteristics of GraphsDate: ______

Identifying Attributes of a Function from Its Graph

Learning Target E:I can identify attributes of a function from its graph.

Use the graph of f(x) to identify the interval(s) or values for each statement. Express your intervals using inequality notation.

Domain: ______Range: ______

Positive and Negative

A) The function is positive on the interval(s): B) The function is negative on the interval(s):

Zeros of a Function

C)The zeros of the function are:

Increasing and Decreasing

D)The function is increasingon the interval(s):D)The function is decreasing on the interval(s):

Turning Pointsand Local Maximumand Local MinimumValues

e. How many local maximum values does the function have? What is the value of f(x) at these points?

f. How many local minimum values does the function have? What is the value of f(x) at these points?

Average Rate of Change

h. Find the average rate of change on the interval .

g.Give two intervals that have the same average rate of change.

Use the graph of f(x) to identify the interval(s) or values for each statement. Express your intervals using inequality notation.

1. The graph of f(x) is given.

a. The function is positive on the interval(s):

b. The function is negative on the interval(s):

c. The zeros of the function are:

d. The function is increasing on the interval(s):

e. The function is decreasing on the interval(s):

f. Identify any local maximum values.

g. Identify any local minimum values.

h. Find the average rate of change on the interval

2. The graph of f(x) is given.

a. The function is positive on the interval(s):

b. The function is negative on the interval(s):

c. The zeros of the function are:

d. The function is increasing on the interval(s): e. The function is decreasing on the interval(s):

f. Identify any local maximum values. g.Identify any local minimum values.

h. Find the average rate of change on the intervals: , , and .

Sketching a Function’s Graph from a Verbal Description

Learning Target F: I can sketch a function’s graph from a verbal description.

The incidence of a disease is the rate at which a disease occurs in a population. It is calculated by dividing the number of new cases of a disease in a given period (typically a year) by the size of the population. To avoid small decimal numbers, the rate is often expressed in terms of a large number of people rather than a single person. For instance, the incidence of measles in the U.S. in 1974 was about 10 cases per 100,000 people.

Reflect. The graph is horizontal from 1979 to 1980. What can you say about the rate of change for the function on this interval?

Your Turn. A grocery store stocks shelves with 100 cartons of strawberries before the store opens. For the first 3 hours the store is open, the store sells 20 cartons per hour. Over the next 2 hours, no cartons are sold. The store then restocks 10 cartons each hour for the next two hours. In the final hour that the store is open, 30 cartons are sold. Sketch the graph of the function.