for a linear function u must have either the domain or the range and use it to find the other
the domain is the values of x and they produce values of y called the range
eg find the range for the eq. f(x)=y=3x+1 0=<x<5
y=1 at x=0 y=16 at x=5
so 1=<f(x)<16
quadratic functions:
the previous method cannot be used because it is in a shape of a curve and it has a max or min value
eg f(x)=y=x^2 + 2 -2<x<4
if u solve it in the prev. method ----> y=6 y=18 and will consequently write that 6<f(x)<18 which is not right
u have to determine the turning point of the curve
the most straightforward method is to find dy/dx and equating it to 0 which will give u the value of x to get the max. or min point
in the example dy/dx=2x
0=2x -----> x=0
y=2 at x=0 therefore the right range is 2=<f(x)<18
hope u find that useful