for f(x)=x^2+1 given the domain (0,1,4), what is the range?
You're being given 3 "x" values and need to determine the range (what "y" values are produced when those "x" values are plugged into the equation in place of "x").
Since f(x) denotes function notation, the f(x) value is the output of the function, or "Y" value.
So we can think of the function as y=x^2+1. Now one at a time we go in and replace the "x" in the equation for the domain values (0,1,4,), and see what Y equals in each case.
f(0): y=(0)^2+1 y=0+1 y=1
f(1): y=(1)^2+1 y=1+1 y=2
f(4) y=(4)^2+1 y=16+1 y=17
So the range is (1,2,17)
Hope this helps!
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