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The complete graph of the function f is ...


The complete graph of the function f is shown in the xy-plane above. Which of the following are equal to 1 ?
I. `f(-4)`
II. `f((3)/(2))`
III. `f(3)`

A

III only

B

I and III only

C

II and III only

D

I, II, and III

Text Solution

Verified by Experts

Choice D is correct. The definition of the graph of a function f in the xyplane is the set of all points (x, f (x)). Thus, for −4 ≤ a ≤ 4, the value of f(a) is 1 if and only if the unique point on the graph of f with x-coordinate a has y-coordinate equal to 1. The points on the graph of f with x-coordinates −4, `(3)/(2)` , and 3 are, respectively, (−4, 1), `((3)/(2),1)` , and (3, 1). Therefore, all of the values of f given in I, II, and III are equal to 1.
Choices A, B, and C are incorrect because they each omit at least one value of x for which f(x) = 1.
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