SOLUTION: A) Find the y intercepts B) Find the x intercepts and C) find the intervals of x where f(x) > 0 and those where f(x) <0. Do not sketch the graph. f(x) = (x-5) (x+4) (x-3)

Algebra ->  Functions -> SOLUTION: A) Find the y intercepts B) Find the x intercepts and C) find the intervals of x where f(x) > 0 and those where f(x) <0. Do not sketch the graph. f(x) = (x-5) (x+4) (x-3)      Log On


   



Question 1025457: A) Find the y intercepts B) Find the x intercepts and C) find the intervals of x where f(x) > 0 and those where f(x) <0. Do not sketch the graph.
f(x) = (x-5) (x+4) (x-3)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A) When x=0,
f%280%29=%28-5%29%284%29%28-3%29=60
B) x-5=0
x=5
and
x%2B4=0
x=-4
and
x-3=0
x=3
C) Break up the number line into regions using the x-intercepts,
Region 1 : ( -infinity,-4)
Region 2 : (-4,3)
Region 3 : (3,5)
Region 4 : (5,infinity)
Pick a point in each region and test the function to see if its greater than or less than zero.
Region 1 : x=-5
f%28-5%29=%28-5-5%29%28-5%2B4%29%28-5-3%29=%28-10%29%28-1%29%28-8%29=-80
Region 2 : x=0
f%280%29=60
Region 3 : x=4
f%284%29=%284-5%29%284%2B4%29%284-3%29=%28-1%29%288%29%281%29=-8
Region 4 : x=6
f%286%29=%286-5%29%286%2B4%29%286-3%29=%281%29%2810%29%283%29=30
So then,
( -infinity%3Cx%3C-4) , f%28x%29%3C0
(-4%3Cx%3C3) f%28x%29%3E0
(3%3Cx%3C5), f%28x%29%3C0
(5%3Cx%3Cinfinity), f%28x%29%3E0