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

Answer 1

Genesis Allen

#[-9/4,oo)#

#"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]}

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Answer 2

Nathan Axel

The range of the function (f(x) = 9x^2 - 9x) is all real numbers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.