Section 1.8 Interpreting Graphs of Functions Algebra 1

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

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

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?

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?

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?

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?

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?

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?

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?

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

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

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

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

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

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