Roman C. answered • 04/25/16
Tutor
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(851)
Masters of Education Graduate with Mathematics Expertise
Increasing x by 1 always decreases y by 1 in this table. Thus the function is linear with slope -1.
Write f(x) = b - x and plug in f(1) = 3.
f(1) = b - 1 = 3
b = 4
Therefore the function is f(x) = 4 - x.
Roman C.
tutor
In the linear function f(x) = mx + b, the number m is the slope. Increasing x by 1, results in adding m to the value of f(x).
In other words, f(x + 1) = f(x) + m.
According to the table, f(x + 1) = f(x) - 1, so m = -1.
Thus our function is f(x) = -x + b
The b is the y-intercept, which is f(0), but since 0 is not shown in the table in the row for the domain, we must choose a different x.
x = 1 is in the table, and there we see that f(1) = 3. So we plug it in.
f(1) = -1 + b = 3 so that b = 4
Thus we see that f(x) = -x + 4
I had it rearranged as f(x) = 4 - x, which is the same.
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04/25/16
Isaac K.
Thank you!
Report
04/25/16
Isaac K.
04/25/16