Library of Functions.

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A Library of Functions This presentation will review the behavior of the most common functions including their graphs and their domains and ranges. See.

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Presentation transcript:

Library of Functions

Constant f (x) x (Output is the same, no matter what the input is) -4 -5 -3 -2 -1 1 2 3 4 5 Constant (Output is the same, no matter what the input is) Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Identity (linear) f (x) x (Input equals output) -4 -5 -3 -2 -1 1 2 3 4 Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Square (quadratic) f (x) x 5 4 3 2 1 Intercepts? Domain? Range? -4 -5 -3 -2 -1 1 2 3 4 5 Square (quadratic) Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Square root f (x) x 5 4 3 2 1 Intercepts? Domain? Range? -4 -5 -3 -2 -1 1 2 3 4 5 Square root Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Cube (cubic) f (x) x -8 -10 -6 -4 -2 2 4 6 8 10 Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -10 -8 -6 -4 -2 0 2 4 6 8 10

Cube root f (x) x -8 -10 -6 -4 -2 2 4 6 8 10 Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -10 -8 -6 -4 -2 0 2 4 6 8 10

Reciprocal f (x) x 5 4 3 2 1 Intercepts? Domain? Range? -4 -5 -3 -2 -1 1 2 3 4 5 Reciprocal Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Absolute value f (x) x (Output is positive version of the input) 5 4 3 -4 -5 -3 -2 -1 1 2 3 4 5 Absolute value (Output is positive version of the input) Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Greatest integer f (x) x 5 4 3 2 1 Intercepts? Domain? Range? -4 -5 -3 -2 -1 1 2 3 4 5 Greatest integer Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5

Circle Not a function! y x 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -5 -4 -3 -2 -1 0 1 2 3 4 5

Semicircle f (x) x 5 4 3 2 1 Intercepts? Domain? Range? -4 -5 -3 -2 -1 1 2 3 4 5 Semicircle Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima? -5 -4 -3 -2 -1 0 1 2 3 4 5