How do you find the domain and range of #5(x - 2) (x + 1)#?

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Answer 1 · 2018-05-23T04:59:45

Domain: #(-oo,+oo)# Range: #[-11.25,+oo)#

Let #f(x) = 5(x-2)(x+1)#

#= 5x^2-5x-10#

#f(x)# is defined #forall x in RR -># Domain: #(-oo,+oo)#

#f(x)# is a quadratic function of the form #ax^2+bx+c#

Since #a>0#, #f(x)# will have a minimum value at #x=(-b)/(2a)#

#(-b)/(2a) = (-(-5))/(2xx5) = 1/2#

#:. f(x)_min = f(1/2)#

#f(x)_min = 5/4 - 5/2 -10 = -5/4 -10 = -45/4#

#= 11.25#

#f(x)# has no finite upper bound.

Hence, Range: #[-11.25, +oo)#

We can visualise the domain and range of #f(x)# from its graph below.

graph{5(x-2)(x+1) [-24.9, 26.43, -14.9, 10.75]}