Algebraic Operations on Functions College Algebra Combine Functions
Algebraic Operations on Functions College Algebra
Combine Functions using Algebraic Operations Calculate how much it costs to heat a house on a particular day of the year: The cost to heat a house will depend on the average daily temperature, and in turn, the average daily temperature depends on the particular day of the year. We have two relationships: 1. The cost depends on the temperature 2. The temperature depends on the day
Composition of Functions •
Evaluating Composite Functions Using Tables • 1 6 3 2 8 5 3 3 2 4 1 7
Evaluating Composite Functions Using Graphs •
Evaluating Composite Functions Using Formulas •
Domain of a Composite Function •
Decomposing a Composite Function •
Graph Functions using Vertical Shifts •
Graph Functions using Horizontal Shifts •
Vertical and Horizontal Reflections •
Vertical and Horizontal Reflections •
Even and Odd Functions •
Vertical Stretches and Compressions •
Horizontal Stretches and Compressions •
Combine Vertical and Horizontal Stretches For a Function and both a Vertical and Horizontal Shift, Sketch the Graph 1. Identify the vertical and horizontal shifts from the formula 2. The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant 3. The horizontal shift results from a constant added to the input. Move the graph left for a positive constant and right for a negative constant 4. Apply the shifts to the graph in either order
Combining Transformations •
Summary: Transformations of Functions Vertical shift Horizontal shift Vertical reflection Horizontal reflection Vertical stretch Vertical compression Horizontal stretch Horizontal compression
Inverse Functions •
Inverse Functions •
Inverse Functions •
Inverse Functions •
Graph a Function’s Inverse •
Quick Review •
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