Find the domain intercepts and turning points of the functio

Find the domain, intercepts, and turning points of the function defined by the graph. Give the intervals for which the function is constant, where it is increasing, and where it is decreasing. (Enter your answers using interval notation).

Solution

a) domain is all x values where graph exists

on looking the graph we can see that domain is [ -7 , + 7 ]

b) x intercept is the point where graph cuts x axis

x intercepts are x = 3 ( smaller x value )

x = 6 ( larger x value )

c) y intercept is the point where graph cuts y axis

y intercept = y = 8

d) x coordinates of turning points are ( 1,3,5 )

e) function is constant from ( x = -7 to x = 1 )

interval [ -7,1]

function is increasing that is going up for ( x = 3 to x = 5)

interval [ 3 , 5 ]

function is decreasing at two intervals from ( x = 1 to x = 3) and from ( x = 5 to x = 7 )

interval [ 1,3] U [ 5,7 ]