1. Section 1.8 Interpreting Graphs of Functions
Algebra 1

2. Welcome back! Warm- up Agenda Pass back quizzes
1.8 Interpreting Graphs
Homework Time
Create the graph for each situation in relation to time:
The height of a ball as a baseball player throws it as high as he can into the air and then hits the ground.
The speed of a car as it gets off the high way, stops at a stop light, and then continues to drive through side streets.

3. Objectives Interpret the context of a graph of functions
Create a graph with given specific conditions

4. Linearity & Intercepts
Linear: the graph of the function is a straight line
Non-Linear: The graph of the function is Not a Straight Line
y=mx+b
y=x² or y=x³

5. Linearity & Intercepts
X- Intercept
Intercepts: points on the graph that intersect an axis.
Y- Intercept

6. Linearity & Intercepts
X-Coordinate: 0 seconds
Y-Coordinate: 20 meters
At 0 seconds the object is 20 meters high. Thus, the object starts at 20 meters above the ground.
Example 1: The graph shows the height 𝑦 of an object as a function of time 𝑥.
A) Is the graph linear or nonlinear?
B) What is the y-intercept? What does it Mean?
C) What is the x-Intercept? What does it mean?
NONLINEAR
X-Intercept: About 𝟖.𝟓, 𝟎
X-Coordinate: 8.5 seconds
Y-Coordinate: 0 Meters
At 8.5 seconds the height is zero. Thus, the object is on the ground.

7. Line Symmetry
Can you draw the other half of the Image?

8. Line Symmetry
A graph has line Symmetry in some vertical line if one half is a mirror image of the other. This graph has Line Symmetry At x = 2.

9. Line Symmetry
Example 1: Let the graph represent an object being launched into the air. What does the symmetry of the graph mean in this context? It took the same amount of Time to go up as it did down

10. Positive & NEgative
Positive: when the function’s graph is above the x-axis.
Negative: When the function’s graph is below the x-axis.

11. Increasing & Decreasing
Increasing: The graph moves up
Decreasing: The graph moves down

12. End Behavior As x-values Increase, Y- Values Increase
Describes the values of a function as x-values become very small and very large
As x-values Decrease,
Y-Values Decrease

13. Extrema Extrema: High or Low function values
Relative Minimum: no other points nearby have a lesser y- coordinate
Relative maximum: no other points nearby have a Greater y-coordinate

14. Comprehensive Example
Positive:
-between 𝑥=−0.6 and 𝑥=10.4
-There were positive sales between
Negative:
- 𝑥<−0.6 and 𝑥>10.4
- The model predicts negative sales after 2010
Comprehensive Example
U.s. retail sales of video games from can be modeled by the function at the right.
A) Estimate and interpret where the function is positive and Negative

15. Comprehensive Example
Increasing:
- and between and
- Sales increased to about and from
Decreasing:
-Between and and
- Sales decreased from and have been decreasing since 2008
Comprehensive Example
B) Estimate and interpret where the graph is increasing and decreasing.

16. Comprehensive Example
Relative Max:
-Around 𝑥=1.5 and 𝑥=8
-The company experienced 2 relative peak in sales in about and 2008
Relative Min:
Around 𝑥=3
The company experienced a relative low in sales in 2003
Comprehensive Example
C) Estimate and interpret where the graph has Relative extrema

17. Comprehensive Example
X-Intercepts:
-Around (−0.6, 0) and (10.4, 0)
-A little after 2010 there were zero sales.
Y-intercepts:
-at (0, 4)
IN 2000, the company had
$4,000,000,000 in sales
Comprehensive Example
d) Estimate and interpret the intercepts of the graph

18. Comprehensive Example
As x increases, y decreases
As x decreases, y decreases
The model indicates there were negative sales prior 2000 and after 2009.
Does this seem like a reliable model?
Comprehensive Example
E) Estimate and interpret The end behavior of the graph

19. Sketching a graph
Sketch a graph of a function that could represent the situation:
1.) A nonlinear graph
2.) Y-intercept at
3.) X-intercept at
4.) When the graph is positive and decreasing
5.) When the graph is negative and decreasing

20. Exit Slip
Please complete the exit slip on your own and place it in the bins on the cabinet door. Be honest with yourself and put it in the appropriate bin.
Homework
1.8 Practice Worksheet ALL