Math 110
In Class Exercises, Section 2.4
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Properties of a function
1) Examine the picture to the left. For these
questions, you may assume that the interval to be
considered is pictured in it's entirely
Where is the function increasing?
Where is the function decreasing?
Where is the function constant?
How many local maxima are there? What are
they?
How many local minima are there? What are
they?
2) Examine the picture to the left. For these
questions, you may assume that the interval to be
considered is pictured in it's entirely
Where is the function increasing?
Where is the function decreasing?
Where is the function constant?
How many local maxima are there? What are
they?
Math 110
How many local minima are there? What are
they?
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X
Math 110
In Class Exercises, Section 2.4
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
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3) Examine the picture to the left.
For these questions, you may
assume that the interval to be
considered is pictured in it's entirely
Where is the function increasing?
2 3 4 5 6 7 8 9 10
Y
Where is the function decreasing?
Where is the function constant?
How many local minima are
there? What are they?
How many local maxima are there? What are they?
Math 110
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Math 110
In Class Exercises, Section 2.4
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X
Average Rate Of Change
Goal: Identify the rate of change of a function, given it's picture ; intuitively understand ARoC
4) What is the average rate of change
between x = -8 and x = -4?
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
Draw the secant line between these
two points on the graph to the left
2 3 4 5 6 7 8 9 10
What is the average rate of change
between x = 2 and x = 3?
Y
X
Draw the secant line between these
two points on the graph to the left
5) What is the average rate of change
between x = -8 and x = -4?
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
Draw the secant line between these
two points on the graph to the left
2 3 4 5 6 7 8 9 10
What is the average rate of change
between x = 4 and x = 6?
Y
Draw the secant line between these
two points on the graph to the left
Math 110
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Math 110
In Class Exercises, Section 2.4
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6) Let's say you were looking at the graph of
1
y  x 2 (pictured left), and wanted to find a
8
formula for the average rate of change between
x=-2, and any other point on the graph.
What is the average rate of change between x = 2 and x = 6?
What is the average rate of change between x = 2 and x = 2?
Using the formula given in class, find a formula
for the average rate of change from x = -2 to any
other point, then use this formula to check your
answers for the prior two questions
7) Let's say you were looking at the graph of
1 3
y
x  2 x 2 (pictured left), and wanted to find a
60
formula for the average rate of change between
x=-2, and any other point on the graph.
Using the formula given in class, find a formula for
the average rate of change from x = 0 to any other
point
Math 110
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