Transformations of the Graphs of Exponential Functions New Mind Map

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Transformations of the Graphs of Exponential Functions New Mind Map by Mind Map: Transformations of the  Graphs of Exponential  Functions New Mind Map

1. Stretches and Compressions of the Parent Function

1.1. f(x)=ab^(x)

1.1.1. when the variable a is |a| > 1 the graph stretches

1.1.2. when the variable a is 0 < |a| < 1 the graph compresses

2. Relfection on Parent Funciton

2.1. Equation for Reflection with respect of x-axis: f(x) = -b^(x)

2.2. Equation for Reflection with respect of y-axis: f(x) = b^(-x) or (1/b)^x

3. Graphing Horizontal Shift

3.1. y = b^(x+c)

3.1.1. when the variable c equals negative shifts right of the x axis

3.1.2. when the variable c equals positive shifts left of the x axis

4. Graphing Vertical Shift

4.1. y = b^(x)+d

4.1.1. when the variable d equals negative shifts downward of y axis

4.1.2. when the variable d equals positive shifts upward of y axis

5. General Form of All Transformations

5.1. f(x)=ab^(x+c)+d

6. Basic properties of Exponential Functions

6.1. Domain of the equation is always (-infi, infi)

6.2. Range of the equation is always ( d, infi / -infi)

6.3. The parent function always passed through (0,1)