What is the average value of y for the range of x shown in the following plot?

Correct option is C

Solution:

The given plot is of the function f(x)=1+|x| in the domain (-1,1)

That is, f(x)=1+x   if x≥0

f(x)=1-x     if x<0

We know that the average value of a function is given by

​$$\text{Average value} = \frac{1}{(a - b)} \int_a^b f(x)\,dx$$

$$\text{Thus, here,} \\\text{Average value} = \frac{1}{1 - (-1)} \left[ \int_{-1}^0 (1 - x)\,dx + \int_0^1 (1 + x)\,dx \right]$$

$$= \frac{1}{2} \left[ \left(1 + \frac{1}{2} \right) + \left(1 + \frac{1}{2} \right) \right]$$

$$= \frac{1}{2} \left[ \frac{3}{2} + \frac{3}{2} \right]$$

$$= \frac{3}{2} = 1.5$$​​​​​​

So, the average value of y for the range of x shown in the given plot is 1.5.