Question

Your friend says two different translations of the graph of the parent linear function can result in the graph of f(x)=x-2.is your friend correct explain why

Answer 1

The given linear function is f(x) = x-2

The parent function of this linear equation is y=x

Your friend's way of explaining this function is not quite correct.

If the transformation in the function is of the form $y=f(x)+c$, then the graphs moves up or down vertically in the y- axis direction depending upon the value of c.

If c>0, then the graph moves up.

If c<0, the graph moves down.

Comparing the given equation $y=x-2$ with $y=f(x)+c$, we notice, c = -2 which is less than 0.

Hence the graph moves down by 2 units.