Use Graphs of Functions

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Presentation transcript:

Use Graphs of Functions 3.12 Use Graphs of Functions Vocabulary For a function f, between any two points (x1, f (x1)) and (x2, f (x2)) is the slope of the line through the two points. Average Rate of Change

Use Graphs of Functions 3.12 Use Graphs of Functions Example 1 Find an average rate of change Find the average rate of change of Average rate of change of f from x1 = -1 to x2 = 1: Average rate of change of f from x1 = 1 to x2 = 2:

Use Graphs of Functions 3.12 Use Graphs of Functions Checkpoint. Find the average rate of change of the function from x1 = -1 to x2 = 0.

Use Graphs of Functions 3.12 Use Graphs of Functions Example 2 Compare average rates of change Compare the average rates of change of the functions from x1 = -3 to x2 = 0. The function is ____________. So the rate of change, _____, is constant. The average rate of change of f from x1 = -3 to x2 = 0 is _____. linear -1 -1 Average rate of change of g from x1 = -3 to x2 = 0: Average rate of change of f from x1 = -3 to x2 = 0:

Use Graphs of Functions 3.12 Use Graphs of Functions Example 3 Solve an equation using a Graph Method 2 Solve the equation by finding the intersection of two graphs. The solution will be the ___________ of the intersection points. x-values Graph both sides of the equation and find the points of intersection. 6 2 -2 -6 -2 The solutions are _____, _____, and _____. 2 -3 -1 1 3

Use Graphs of Functions 3.12 Use Graphs of Functions Checkpoint. Solve the equation by graphing. -2 The solutions are _____, and _____.

Use Graphs of Functions 3.12 Use Graphs of Functions Checkpoint. Solve the equation by graphing. 3 The solutions are _____, and about _____. 5.4

Use Graphs of Functions 3.12 Use Graphs of Functions