For the graph gx below find the indicated information Write

For the graph g(x) below, find the indicated information. Write answers in interval notation where appropriate. Find g(5). State the intervals of x where the graph is increasing State the intervals of x where the graph a decreasing. State the interval of x where the graph is constant. State the coordinates of the x-intercept(s). State the coordinates of the y-intercept. g. State the domain in interval notation. h. State the range in interval notation. i. Find any relative maxima. j. Find any relative minima.

Solution

a) g(5)

that is function value at x = 5

g(5) = 2

b) intervals of increasing that is going up

[ - 3 , 2 ] U [ 4,6]

c) intervals of decreasing that is graph going down

[ -5 , -3 ] U [ 6 , 7 ]

d) interval of constant that is graph is constant

[ 2,4 ]

e) coordinates of x intercepts ( points where graph cuts x axis )

( - 5,0 ) and ( 1, 0 )

f) y intercept ( points where graph cuts y axis )

( 0 , -1 )

g) domain is all x values where graph exists

domain is [ -5 , 7 ]

h) range is all y values where graph exists

range is [ 3,-4]

i) relative maxima at (6,3)

j) relative minima at (-3, -4 )