1. Interpreting Graphs of Functions

2. Vocabulary X-intercept – where the graph crosses the x-axis.
Y-intercept – where the graph crosses the y-axis.
(0, y)
Example: Find the x- and y- intercepts of the graph.
X-intercepts (-2, 0) and (2, 0)
Y-intercept (0, -4)

3. Vocabulary [1,3.5] [-.5,1] and [3.5,7]
Interval – A section of the graph.
Define intervals by x values.
At which x value does the section start and stop?
To state an interval: [starting x value, ending x value]
Increasing Intervals –
A function is “increasing” when the y-value increases as the x-value increases.
When is the graph ‘going up’?
This function is increasing for the interval shown. It may be increasing or decreasing elsewhere.
Decreasing Intervals –
A function is “decreasing” when the y-value decreases as the x-value increases
When is the graph ‘going down’?
[1,3.5]
[-.5,1]
and [3.5,7]

4. Find where the function is increasing or decreasing.
To state an interval:
[starting x value, ending x value]
The graph is increasing in the following intervals:
[-2.2, -1.2]
[1.2, 2.2]
The graph is decreasing in the following interval:
[-1.2, 1.2]

5. Vocabulary
Relative Minimum – the smallest value of the function within an interval.
Lowest point (a y value)
What is the minimum value in the interval [1, 5]?
The minimum value is 1 because between where x is 1 and where x is 5, the lowest y value is 1
Relative Maximum – the largest value of the function within the interval.
Highest point (a y value)
What is the maximum value in the interval [1, 5]?
The maximum value is 4.5

6. Has an absolute max.
Does not have absolute min.
Parabolas (u shape) go on forever in one direction
Vocabulary
Absolute Minimum – a function has an absolute min. if there is a point whose y-coordinate is less than the y of every other point on the graph.
The “lowest” spot on the entire graph
It doesn't “go down forever”
Absolute Maximum – a function has an absolute max. if there is a point whose y-coordinate is greater than the y of every other point on the graph
The “highest” spot on the entire graph
It doesn’t “go up forever”
Has an absolute min.
Does not have absolute max.
Absolute value fcts (v shape) go on forever in one direction
Doesn’t have an absolute max. or absolute min.
Linear functions (lines) go on forever in each direction

7. Identify the features of the function.
Find the x-intercepts:
(-8, 0), (-3, 0), (8, 0)
Find the y-intercept:
(0, -4)
Name the intervals where the function is increasing:
[-8, -6], [6, ∞]
Name the intervals where the function is decreasing:
[-6, 0], [4, 6]
Name the interval where the function is constant (flat):
* Remember to write intervals by [starting x value, ending x value]
[0, 4]

8. Identify the features of the function.
Name the maximum for the interval [-8, -5]: 7
Name the minimum for the interval [2, 8]: -8