1. Section 1.8 Interpreting Graphs of Functions
Algebra 1

2. Learning Targets
Define vocabulary terms: intercepts, y-intercept, x-intercept, end behavior, linear, non-linear, positive, negative, increasing, decreasing, extrema, relative minimum, relative maximum, continuous
Identify the intercepts from the graph of a function
Interpret the intercepts in a context
Determine and interpret where a graph is positive and negative
Determine and interpret where a graph is increasing and decreasing
Determine and interpret where a graph has a relative minimum/relative maximum
Describe the end behavior of a graph
Create a graph with given specific conditions

3. Define Graph characteristics
y-intercept
x-intercept
Linear
Non-Linear
Positive
Negative
Increasing
Decreasing
end behavior
relative minimum
relative maximum
continuous
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph? Have students draw all of these characteristics on the first and second graph

5. Identify: Example 1 Answer the following questions:
Linear or Non-Linear?
Non-Linear
Where is the graph increasing?
From 𝑥<0
Where is the graph decreasing?
From 𝑥>0
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

6. Identify: Example 2 Answer the following questions:
What is the end behavior of the graph?
As x-values increase and decrease, y-values decrease.
Where is there a relative extrema? What type is it?
At 𝑥=0, relative max
Is the graph continuous?
Yes
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

7. Identify: Example 3 Answer the following questions:
What is the x-intercept?
(−1, 0)
What is the y-intercept?
(0, 2)
Linear or Non-Linear?
Linear
Where is the graph positive?
From 𝑥>−1
Where is the graph negative?
From 𝑥<−1
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

8. Math Challenge
In your groups, create a graph with the following conditions. There are many answers
1. The x-intercepts are at −1, 0 , 0, 0 , (1, 0)
2. The graph is positive from 𝑥=0 to 𝑥=1
3. As x-values increase, y-values decrease
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

9. Math Challenge One possible answer:
1. The x-intercepts are at −1, 0 , 0, 0 , (1, 0)
2. The graph is positive from 𝑥=0 to 𝑥=1
3. As x-values increase, y-values decrease
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

10. Exit Ticket for Feedback
Identify the following from the graph.
End Behavior
X-Intercept & Y-Intercept
Positive
Decreasing
Relative Minimum
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

11. Resources The following are slides for reference
Why might we want to know these characteristics of a graph? What can they tell us about the information constructing the graph?

12. Linearity & Intercepts
Linear: the graph of the function is a straight line
Non-Linear: The graph of the function is Not a Straight Line

13. Linearity & Intercepts
Intercepts: points on the graph that intersect an axis.
X-intercept:
Roots
solutions when y=0
X- Intercept
Y- Intercept

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

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

16. 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

17. 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