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Question: The graph of a function f is given.
Page in 8th Edition: 19
Short Answers:
 f(1) = 3
 f(1) ~ .3
 f(x)=1 for x = 0 or 3
 f(x)=0 for approximately x=0.6
 The domain of x are real numbers between 2 and 4 (or [2,4], and the range are real numbers between 1 and 3, or [1,3].
 f is increasing on the interval [2,1)
Homework Answer: Same as Short Answers.
Motivated Answers:
The question is giving you the graph of the function f. This means that to figure out what f(x) is, we need to look at the yvalue of the graph at x.

To figure out f(1), we can take put a ruler vertically (up down) on the graph when x=1 and see how high the graph is, which is the same thing as the yvalue of the graph. We can count boxes on the graph paper to see the yvalue is 3.

Just like a), we put a ruler vertically at x=1, and the graph seems to show a yvalue of about .3 (it could be 0.2 or 0.5, but that’s our best guess by eyeballing it). This means f(1)~0.3

The question wants us to find all values of x where f(x)=1. Since 1 is the output of f, and the output means to yvalues, we can take a ruler, put it horizontally at 1, and look at where the ruler hits the graph. We see the rule hits the graph two times, once when x is 0, and another time when x = 3.

We do the same thing as c), but put the ruler horizontally at 0, which happens to be the xaxis. The graph hits the ruler at x=.6 approximately.

You have to find the domain and range of f. The domain of any function is all valid inputs, or stated the same way, all valid xvalues. We can see from the graph that the graph spans the xrange of 2 though 4 (we can count boxes). To write this in interval notation, we write the range is [2,4]. We use solid brackets here because the graph seems to include the endpoints. The range of f is all valid outputs of f. Stated the same way, these are all valid yvalues of the graph. We can see the graph spans the yrange of 1 through 3, or [1,3].

If you look at the graph you can see that f seems to be increasing throughout the first part of it, from xvalues of 2 to 1. Writing this in interval notation, we get [2,1). We use a parenthesis ) instead of bracket ] because at the point 1, the function is no longer increasing.
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