ws04 - WORKSHEET 4 Fall 1995 1 The graph of f(x is given...

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WORKSHEET 4 - Fall 1995 1. The graph of f ( x ) is given below. Use it to graph the following: a) f (3 x ) e) f ( x ) + 1 b) f ( x ) f) 5 f ( x ) c) f ( 2 x ) g) f ( x + 2) d) f ( x 1) h) 5 f (3 x + 2) + 1 i) In your own words, describe the manner in which the graph of f ( x ) changes when we multiply f ( x ) by a constant; add a constant to f ( x ); multiply x by a constant; add a constant to x . j) Describe the process of drawing u ( x ) = af ( bx + c ) + d , where a , b , c , and d , are constants when given only the graph of f ( x ). 2 -2 2 -2 x f(x) 2. A one-sided limit is a limit in which we consider approaching a point from only one side while ignoring the other side. We use the notation x a + to mean x a restricted so that x > a, x a to mean x a restricted so that x < a. We then have the following one-sided limits: Right-Hand Limit lim x a + f ( x ) means lim x a x>a f ( x ) . Left-Hand Limit lim x a f ( x ) means lim x a x<a f ( x ) . a) Use the graph of f ( x ) in Problem 1 to determine i) lim x →− 7 f ( x ) ii) lim x →− 7 + f ( x ) iii) f ( 7) iv) lim x →− 7 f ( x
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