Section 1.8 Interpreting Graphs of Functions Algebra 1

Welcome back! Warm- up Agenda Pass back quizzes/Quiz corrections Updated grades. 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.

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

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

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

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.

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

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.

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

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

Comprehensive Example Positive: -between 𝑥=−0.6 and 𝑥=10.4 -There were positive sales between 2000-2010 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 2000-2009 can be modeled by the function at the right. A) Estimate and interpret where the function is positive and Negative

Comprehensive Example Increasing: - 𝑥<1.5 and between 𝑥=3 and 𝑥= 8 - Sales increased to about 2002 and from 2003-2008 Decreasing: -Between 𝑥=1.5 and 𝑥=3 and 𝑥> 8 - Sales decreased from 2002-2003 and have been decreasing since 2008 Comprehensive Example B) Estimate and interpret where the graph is increasing and decreasing.

Comprehensive Example Relative Max: -Around 𝑥=1.5 and 𝑥=8 -The company experienced 2 relative peak in sales in about 2002 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

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

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

Sketching a graph Sketch a graph of a function that could represent the situation: The balance due on a car loan from the date the car was purchased until it was sold 4 years later

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

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