Learn how to graph exponential functions using transformations with this detailed tutorial from Mario's Math Tutoring! We'll break down the y = a * b^(x-h) + k form, explaining how each parameter affects the graph, including shifts, stretches, shrinks, and reflections.
You'll discover:
Base (b): How 'b' determines if the function is exponential growth or decay.
Coefficient (a): The effect of 'a' on vertical stretches/shrinks and reflections over the x-axis.
Horizontal Shift (h): How x-h shifts the graph left or right (remember the opposite effect!).
Vertical Shift (k): How 'k' shifts the graph up or down, and where it defines the horizontal asymptote (y = k).
Step-by-Step Graphing: We'll use tables to track transformations from the parent function to the final graph.
We'll work through three examples, including both growth and decay functions, to help you master graphing exponential functions.
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