 A function that can be expressed in the form and is positive, is called an Exponential Function.  Exponential Functions with positive values of x are.

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 A function that can be expressed in the form and is positive, is called an Exponential Function.  Exponential Functions with positive values of x are increasing, one-to-one functions.  The parent form of the graph has a y-intercept at (0,1) and passes through (1,b).  The value of b determines the steepness of the curve.  The function is neither even nor odd. There is no symmetry.  There is no local extrema.

 The domain is  The range is  End Behavior:  As  The y-intercept is  The horizontal asymptote is More Characteristics of There is no x-intercept. There is no x-intercept. There are no vertical asymptotes. There are no vertical asymptotes. This is a continuous function. This is a continuous function. It is concave up. It is concave up.

 How would you graph Domain: Range: Y-intercept: Domain: Range: Y-intercept: Inc/dec? Horizontal Asymptote: Horizontal Asymptote: Concavity?  How would you graph up increasing up

 Recall that if then the graph of is a reflection of about the y-axis.  Thus, if then Domain: Range: Y-intercept: Horizontal Asymptote: Concavity? up

 Notice that the reflection is decreasing, so the end behavior is: Is this graph increasing or decreasing? Decreasing.  How would you graph

Exponential graphs, like other functions we have studied, can be dilated, reflected and translated. It is important to maintain the same base as you analyze the transformations. Vertical shift up 3 x-axis Vertical stretch 3 Vertical shift down 1

Reflect about the x-axis. Horizontal shift right 1. Vertical shift up 1. Vertical shrink ½. Horizontal shift left 2. Vertical shift down 3. Domain: Range: Y-intercept: Horizontal Asymptote: Inc/dec? Concavity? Domain: Range: Y-intercept: Horizontal Asymptote: Inc/dec? Concavity? decreasing down increasing up