Stewart’s Calculus 8th Edition, Section 1.1, Question 3

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Question: The graph of a function f is given.

Page in 8th Edition: 19

Short Answers:

1. f(1) = 3
2. f(-1) ~ -.3
3. f(x)=1 for x = 0 or 3
4. f(x)=0 for approximately x=-0.6
5. 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].
6. 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 y-value of the graph at x.

1. 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 y-value of the graph. We can count boxes on the graph paper to see the y-value is 3.

2. Just like a), we put a ruler vertically at x=-1, and the graph seems to show a y-value 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

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 y-values, 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.

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

5. 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 x-values. We can see from the graph that the graph spans the x-range 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 y-values of the graph. We can see the graph spans the y-range of -1 through 3, or [-1,3].

6. If you look at the graph you can see that f seems to be increasing throughout the first part of it, from x-values 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.

Video Solution:

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