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THE SQUARE ROOT FUNCTION Properties of 1. The domain and range are both the set of Section 3.4 nonnegative real numbers; that is, 0, ∞ . 2. The ‐intercept of the graph is 0, 0 . The ‐intercept of the graph is also Library of Functions; 0, 0 . Piecewise-Defined Functions 3. The function is neither even nor odd. 4. It is increasing on the interval 0, ∞ . 5. It has a local minimum of 0 at 0.
THE ABSOLUTE VALUE THE CUBE ROOT FUNCTION FUNCTION Properties of Properties of 1. The domain is the set of all real numbers; 1. The domain and range are the set of all that is, ∞, ∞ . The range is all real numbers; that is, ∞, ∞ . nonnegative real numbers; that is, 0, ∞ . 2. The ‐intercept is 0, 0 . The ‐ 2. The ‐intercept of the graph is 0, 0 . The intercept is also 0, 0 . ‐intercept of the graph is also 0, 0 . 3. The function is odd. 3. The function is even. 4. It is increasing on the interval ∞, ∞ . 4. It is decreasing on the interval ∞, 0 . It 5. It does not have a local minimum or a is increasing on the interval 0, ∞ . local maximum. 5. It has a local minimum of y 0at 0.
LIBRARY OF FUNCTIONS LIBRARY (CONTINUED) 1. Constant Function: 3. Linear Function: Domain: ∞, ∞ Domain: ∞, ∞ Its graph is a horizontal line. Its graph is a line. Its ‐intercept is 0, . Its ‐intercept is 0, . It is constant on the entire domain. Increasing if 0. Decreasing if 0. It is the constant function if 0. It is the identity function if 1 and 0. 2. Identity Function: 4. Square Function: Domain: ∞, ∞ Domain: ∞, ∞ Its graph is a line. Its graph is a parabola. Its y‐intercept is 0, 0 . Its y‐intercept is 0, 0 . It is increasing on the entire domain. It is decreasing on ∞, 0 and increasing on 0, ∞).
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LIBRARY (CONTINUED) LIBRARY (CONTINUED) 5. Cube Function: 7. Cube Root Function: Domain: ∞, ∞ Domain: ∞, ∞ Its ‐intercept is 0, 0 . Its ‐intercept is 0, 0 . It is increasing on ∞, ∞ . It is increasing.
8. Reciprocal Function: 6. Square Root Function: Domain: ∞, 0 ∪ 0, ∞ Domain: 0, ∞ It has no intercepts. Its graph is a half parabola. It is decreasing on the intervals ∞, 0 and 0, ∞ . Its ‐intercept is 0, 0 . It is increasing on the interval 0, ∞ .
PIECEWISE-DEFINED LIBRARY (CONTINUED) FUNCTIONS 9. Absolute Value Function: Domain: ∞, ∞ A piecewise‐defined function is a function Its ‐intercept is 0, 0 . that is defined by more than one equation. An It is decreasing on the interval ∞, 0 and example is increasing on the interval 0, ∞ .
10. Greatest Integer Function: int 1 if 1 Domain: ∞, ∞ if 1 1 It is an example of a step function. 2 if 1 Its ‐intercept is 0, 0 . It is constant on the intervals , 1 where is any integer.
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