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# Characteristics of Function Graphs

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by

## Juan Jorrin

on 1 November 2016

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#### Transcript of Characteristics of Function Graphs

Attributes of a Function from its Graph
Relative Extreme Values
Points on the function graph where the function changes from decreasing to increasing or vise versa.
Sketching a Function's Graph from a Verbal Description
Sketch a graph of the following verbal description
Lyme disease is a bacterial infection transmitted to humans by ticks. when an infected tick bites a human, the probability of transmission is a function of the time since the tick attached itself to the skin. During the first 24 hours, the probability is 0%. During the next three 24-hour period, the rate of change in the probability is always positive, but it is much greater for the middle period than the other two periods. After 96 hours, the probability is almost 100%. Sketch a graph of the function for the probability of transmission.
Characteristics of Function Graphs
Analyze the graph.
a
b
c
The function is increasing on (a,b)
The function is decreasing at (b,c)
Every graph has an increasing or decreasing point.
the function is increasing at interval
(0,2), (4,6), (8,10)
the function is decreasing at interval
(2,4), (6,8), (10,11)
Let us specify...
Minimum Value
the lowest decreasing point of the function.
Maximum Value
the highest increasing point of the function.
Identify the axes and scales
x - axis
time (in hours)
from 0 to at least 96
y - axis
probability of infection (in percent)
from 0 to 100
Identify key intervals
Intervals are in increments of 24 hours:

0 to 24, 24 to 48, 48 to 72, 72 to 96, and 96 to 120.
Sketch the graph of the function
Draw a horizontal segment at y = 0 for the first 24-hour interval.
Continue plotting the points.
After 96 hours, the graph is nearly horizontal at 100%.
Identify key intervals.
Sketch the graph of the function.
Identify the axis and scales.
Thank you!
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