Question

What transformations was not done to the linear parent function, f(x)=x to get the function g(x)=-1/3(x-7)+2?

Answer 1

Explanation:

Consider that by changing the the variable x with x-c represents a horizontal shift of c units. If c>0 then it is a right shift and it is a left shift otherwise. When we multiply the variable by a number d (i.e dx) we are applying an horizontal compression/stretching. If d>1 it compresses it, and if 0<d<1 it stretches it. By multipyling the variable x by a negative sign, we are reflecting with respect the x -axis. Finally when we add a number to the function, we are applying a vertical shift.

original function x.

1. (x-7): horizontal shift of 7 units to the right.

2. 1/3(x-7): Horizontal stretching by factor 1/3.

3.-1/3(x-7): Reflection with respect the x-axis

4.-1/3(x-7)+2: Vertical shift of two units up.