![]() 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. We can see the graph spans the y-range of -1 through 3, or. Stated the same way, these are all valid y-values of the graph. We use solid brackets here because the graph seems to include the endpoints. The range of f is all valid outputs of f. To write this in interval notation, we write the range is. ![]() We can see from the graph that the graph spans the x-range of -2 though 4 (we can count boxes). The domain of any function is all valid inputs, or stated the same way, all valid x-values. You have to find the domain and range of f. The graph hits the ruler at x=-.6 approximately. We do the same thing as c), but put the ruler horizontally at 0, which happens to be the x-axis. We see the rule hits the graph two times, once when x is 0, and another time when x = 3. 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. The question wants us to find all values of x where f(x)=1. 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). We can count boxes on the graph paper to see the y-value is 3. 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. This means that to figure out what f(x) is, we need to look at the y-value of the graph at x. The question is giving you the graph of the function f. The domain of x are real numbers between -2 and 4 (or, and the range are real numbers between -1 and 3, or.Question: The graph of a function f is given. I’ve read the whole chapter of the text beforehand and spent a good amount of time thinking about what the best explanation is and what sort of solutions I would have wanted to see in the problem sets I assigned myself when I taught. I’ve racked up hundreds and hundreds of hours of experience working with students from 5 th grade through graduate school, and I’m passionate about teaching. Fred Zhang, and I have a bachelor’s degree in math from Harvard. This posts contains a Teaching Explanation.
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