Analyzing graphs

Analyzing graphs Objective: identify key features of a graph and use them to sketch a picture What are the 7 key features of a graph?

Key Features of a Graph #1 Roots (x-intercepts/zeros) • Where does the graph cross the x axis?

#2 Y-intercepts • Where does the graph cross the y axis?

#3 Intervals Increasing/Decreasing From “where” to “where” is the graph increasing &decreasing? ( from left to right)

#4 Local Maximums & Minimums • Where are the “turning points” ? • What are the highest & lowest values?

#5 Continuity Where do any breaks in the graph occur?

#6 End Behavior • What “direction” does the graph go towards at the right end/left end?

ODD (symmetric about origin) EVEN (symmetric about y-axis) #7 Symmetry

Describe the graph below:

I’m thinking of a graph… • Roots @ -4, -1, 2 • Y-intercept at -2 • Inc. , then dec, then inc • Max apprx 2.5 , Min apprx -2.5 • Continuous • Not symmetric • End behavior on left: -∞ • End behavior on right: +∞

I’m thinking of a graph… • Does not have any roots • Y-intercept at 3 • Always increasing • Minimum at 3, No maximum • Continuous • Not symmetric • End behavior on left: none • End behavior on right: +∞ • Parent function: √x

Does not have any roots • Y-intercept at 2 • Dec. until 2, then inc. • Minimum at 2, No maximum • Continuous • Even • End behavior on left: +∞ • right: +∞ • Parent function: |x| I’m thinking of a graph…

I’m thinking of a graph… • Has two roots • Y-intercept is positive • Increases until 0, then dec. • Even

I’m thinking of a graph… • Has three roots • Y-intercept is (0,0) • Min is negative, max is postive • Dec, inc, dec. • Odd • End behavior left: +∞ • right: -∞

I’m thinking of a graph… • Does not have any roots • Does not have a y-intercept • Inc. until x = 0, then dec. • No min, no max • Has a break at the x-axis • Even • End behavior on left: 0 • right: 0

Analyzing graphs