Consider the following graph of fx Determine the average rat

Consider the following graph of f(x) Determine the average rate of change between x = -4 and x = 2. Graph g(x) = f(x) + 3 on the same set of axes. Label the graph as g (x). Graph h(x) = f(x + 6) on the same set of axes. Label the graph as h(x). Graph f^-1(x) on the same set of axes and label as f^-1(x). Use your graphs to determine (f - g)?(-2) Use your graphs to determine (f - g)(-4) Use your graphs to determine (f. h)(1) Determine f(f-1(3/2)).

Solution

a)rate of change is given by change in y co-ordinates by x co-ordinates

5-2/-4-2=3/-6= -1/2 =-0.5

b)calculate the values of g(x) and plot the graph.

g(x)=f(x)+3

g(0)=f(0)+3= 4+3=7

g(2)=f(2)+3=2+3=5

g(-4)=f(-4)+3=5+3=8

g(7)=f(7)+3=0+3=3 plot these.

C) shift the above graph on y-axis for six units you will get h(x)

by drawing the graphs you can determine the values and verify with theoritical values.