2.5 Transformations and Combinations of Functions.

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Presentation transcript:

2.5 Transformations and Combinations of Functions

Vertical Shift Up Y=f(x) Y=f(x)+c

Vertical Shift Down Y=f(x) Y=f(x)-c

Horizontal Shift to the Left Y=f(x) Y=f(x+c)

Horizontal Shift to the Right Y=f(x) Y=f(x-c)

Study Tip We know that positive numbers are to the right of zero on a number line and negative numbers are to the left of zero. This positive-negative orientation does not apply to horizontal shifts. A positive number causes a shift to the left and a negative number causes a shift to the right.

Reflection About the x-Axis Y=f(x) Y=-f(x)

Reflection About the y-Axis Y=f(x) Y=f(-x)

Vertical Stretching and Shrinking Graphs

Y=f(x) Y=1/2f(x) Y=2f(x)

Summary of Transformations c represents a positive real number.

The Sum of Functions

The Difference of Functions

The Product of Functions

The Quotient of Functions