Question

Can someone help me find identify the range?​

Answer 1

Range = $(-\infty, 3]$

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Explanation:

The idea is to plug in the smallest value of the domain, which is x = 1, to get

f(x) = -2x+5

f(1) = -2(1)+5

f(1) = 3

Showing that y = 3 is the largest value in the range. Any larger x value produces a smaller y value. Eg: x = 2 leads to f(2) = 1

So the range is the set of y values such that $y \le 3$ which converts to the interval notation $(-\infty, 3]$. This is the interval from negative infinity to 3.

The square bracket says to include the endpoint while the curved parenthesis means we exclude the endpoint. We always exclude infinity as we can't ever reach it.