Question

What is the linear functions f with the values f (-6) = 10 and f (2) = 10?

Answer 1

Given:

f (-6) = 10 and f (2) = 10?

To find:

The linear function f.

Solution:

If f(x)=y, then the function passes through (x,y).

We have, f (-6) = 10 and f (2) = 10, it means the function passes through (-6,10) and (2,10). So, the equation is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-10=\dfrac{10-10}{2-(-6)}(x-(-6))$

$y-10=\dfrac{0}{2+6}(x+6)$

$y-10=0$

Adding 10 on both sides, we get

$y=10$

Function form is

$f(x)=10$

Therefore, the required function is $f(x)=10$. It is a constant function.