Given the polynomial function fxxx1x7x6 a Find xintercepts w

Given the polynomial function f(x)=x(x-1)(x+7)(x-6)

(a) Find x-intercepts (write your answer from the smallest to the largest number)

(b) Find y-intercept

Solution

An x-intercept is a point on the graph where y or f (x) = 0. Now f (x) = o means x( x -1)(x + 7) ( x - 6) = 0. This means that either x = 0 or x = 1 or x = - 7 or x = 6. Thus the x -intercepts , from the smallest to the largest numbers, are x = - 7, x = 0 , x = 1 and x = 6. Thex- intercept poinr are ( -7 , 0), ( 0, 0), ( 1 , 0) and ( 6, 0)

A y -intercept is a point on the graph where x = 0. Now when x = 0, f (x) = x ( x - 1)(x+7)(x-6) = 0. Thus the y-intercept is y = 0. The y-inyercept point is ( 0 , 0)