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

Answer:

The linear function is given by:

       $y=\dfrac{3}{2}x-\dfrac{7}{2}$

Step-by-step 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:

$m=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\m=\dfrac{-2-(-5)}{1+1}\\\\\\m=\dfrac{-2+5}{2}\\\\\\m=\dfrac{3}{2}$

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 $m=\dfrac{3}{2}$

Hence, the equation of linear function is:

$y-(-2)=\dfrac{3}{2}\times (x-1)\\\\\\y+2=\dfrac{3}{2}x-\dfrac{3}{2}\\\\\\y=\dfrac{3}{2}x-\dfrac{3}{2}-2\\\\\\y=\dfrac{3}{2}x-\dfrac{7}{2}$