Question

What is the range of f(x)=(5x^2-20)/(x-2)??

Answer 1

factor for this one

Answer 2

\[f(x)=\frac{5x^2-20}{x-2}=\frac{5(x+2)(x-2)}{x-2}=5(x+2)\] so long as \(x\neq 2\)

Answer 3

if \(x=2\) the original expression is undefined
the range of \(f(x)=5(x+2)\) is all real numbers, because it is a line.
however, since you are not allowed to replace \(x\) by \(2\) the range skips the value you would get when \(x=2\)

Answer 4

if you replace \(x\) by \(2\) in the line, you get
\[f(2)=5(2+2)=20\] and that is the value that is omitted, since \(x\neq 2\) so the range is all real numbers except \(20\)

Answer 5

thank you so much!!