Question 942994: Suppose f is the function whose domain is the interval [−2, 2], with f defined by the following formula:
f (x) = -x/3, if−2≤x<0
2x , if 0≤x≤2.
(a) Sketch the graph of f .
(b) Explain why the graph of f shows that f is not
a one-to-one function.
(c) Give an explicit example of two distinct numbers
a and b such that f (a) = f (b).
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! a) Not sure how to graph here, but it's not hard to graph on paper. Just graph y = -x/3 but only where x is in [-2,0) and y = 2x where x is in [0,2].
b) You can draw a horizontal line that intersects the graph of f(x) in two places.
c) For example, if a = -1 and b = 1/6, then f(a) = f(-1) = -(-1)/3 = 1/3 and f(b) = f(1/6) = 2*1/6 = 1/3.
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