Bell Ringer What is a function?

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Presentation transcript:

Bell Ringer 10-4-16 1. What is a function? 2. What “test” can you use to determine if a graph is a function? 3. What is domain? 4. What is range?

Graphing Polynomial Functions Tuesday, October 4, 2016

Steps for Graphing Polynomial Functions 1. Find all real zeros and plot the x-intercepts. 2. Substitute zero for x to find the y-intercept and plot it. 3. Estimate the maxima and minima (aka turning points) using a graphing calculator and plot the turning points.. 4. Determine end behavior and draw those segments with arrows. 5. Draw the rest of the function as a smooth curve.

How to determine End Behavior 1. Is the degree of the function an odd number or an even one? 2. Is the leading coefficient positive or negative? 3. Use the chart.

1. f(x) = x4 + x3 – 4x2 – 4x 2. f(x) = x3 – 5x2 + 3x + 2 Examples: list (1-4) the 1) Zeros, 2) y-intercept, 3) maxima and minima, 4) End Behavior, 5) Sketch the graph. 1. f(x) = x4 + x3 – 4x2 – 4x 2. f(x) = x3 – 5x2 + 3x + 2 3. f(x) = -x4 – 7x2 + x + 5 4. f(x) = -x3 – x2 + 1

Classwork and Homework Classwork: Algebra II book p. 356 #13-26 For each problem, list (1-4) the 1) Zeros, 2) y-intercept, 3) maxima and minima, 4) End Behavior, and 5) sketch the graph. Homework: Graphing Polynomial Functions Make sure to follow directions!

Exit Ticket 1. Explain how to determine end behavior. 2. If a polynomial has 8 turning points, what is the least degree it could be?