Question

Graph a linear function which has a rate of change equal to the average rate of change of function f on the interval [-1, 1]. The linear function should pass through the point (1,-2).

Answer 1

The linear function is given by:

`y=(3)/(2)x-(7)/(2)`

Explanation:

It is given that the rate of change of the linear function is equal to the average rate of change of function f on the interval [-1, 1].

The slope(m) or average rate of change of the linear function will be:

`m=(f(1)-f(-1))/(1-(-1))\\\\\\m=(-2-(-5))/(1+1)\\\\\\m=(-2+5)/(2)\\\\\\m=(3)/(2)`

and the linear function pass through (1,-2)

We know that the equation of a line with given slope m and passing through point (a,b) is given by:

Here (a,b)=(1,-2)

and
`m=(3)/(2)`

Hence, the equation of linear function is:

`y-(-2)=(3)/(2)* (x-1)\\\\\\y+2=(3)/(2)x-(3)/(2)\\\\\\y=(3)/(2)x-(3)/(2)-2\\\\\\y=(3)/(2)x-(7)/(2)`