Section 3.2 class notes_2

# Section 3.2 class notes_2 - Section 3.2 Properties of a...

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Section 3.2 Properties of a Function’s Graph Objective 1: Determining the Intercepts of a Function An intercept of a function is a point on the graph of a function where the graph either crosses of touches a coordinate axis. There are two types of intercepts: 1) The y -intercept, which is the y -coordinate of the point where the graph crosses or touches the y -axis. 2) The x -intercepts, which are the x -coordinates of the points where the graph crosses or touches the x- axis. The y -intercept : A function can have at most one y -intercept. The y -intercept exists if 0 x = is in the domain of the function. The y- intercept can be found by evaluating (0). f The x -intercept(s): A function may have several (even infinitely many) x -intercepts. The x -intercepts, also called real zeros, can be found by finding all real solutions to the equation ( ) 0 f x = . Although a function may have several zeros, only the real zeros are x -intercepts. Objective 2: Determining the Domain and Range of a Function from its Graph The domain is the interval [ , ) a b while the range is the interval [ ] , c d .

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