Question

What is the range of the function `f(x) = 9x^2 - 9x`?

Answer 1

`[-9/4,oo)`

Explanation:

`"since the leading coefficient is positive "`

`f(x)" will be a minimum "uuu`

`"we require to find the minimum value"`

`"find the zeros by setting "f(x)=0`

`rArr9x^2-9x=0`

`"take out a "color(blue)"common factor "9x`

`rArr9x(x-1)=0`

`"equate each factor to zero and solve for x"`

`9x=0rArrx=0`

`x-1=0rArrx=1`

`"the axis of symmetry is at the midpoint of the zeros"`

`rArrx=(0+1)/2=1/2`

`"substitute this value into the equation for minimum value"`

`y=9(1/2)^2-9(1/2)=9/4-9/2=-9/4larrcolor(red)"min. value"`

`rArr"range "y in[-9/4,oo)`
graph{9x^2-9x [-10, 10, -5, 5]}