Stitz-Zeager_College_Algebra_e-book

# In general shifting a function vertically like this

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Unformatted text preview: . What’s unique about the point (0, −4) on this graph? Also ﬁnd the intervals on which g is increasing and those on which g is decreasing. y 5 4 3 2 1 −3 −2 −1 −1 −2 −3 −4 1 2 3 x 80 Relations and Functions (c) We said earlier in the section that it is not good enough to say local extrema exist where a function changes from increasing to decreasing or vice versa. As a previous exercise showed, we could have local extrema when a function is constant so now we need to examine some functions whose graphs do indeed change direction. Consider the functions graphed below. Notice that all four of them change direction at an open circle on the graph. Examine each for local extrema. What is the eﬀect of placing the “dot” on the y -axis above or below the open circle? What could you say if no function value was assigned to x = 0? y y 4 4 3 3 2 2 1 1 −2 −1 −1 i. 1 2 x −2 −1 −1 iii. Function I y 2 x Function III 4 5 3 3 1 y 4 2 2 −2 −1 −1 1 2 1 x −2 −1 ii. 1 Function II iv. 1 2 Function IV x 1.7 Graphs of Func...
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