I have a question about how to do graph transformation.

Question

A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph.

f(x) = |x|; shrink vertically by a factor of 1 3 , shift 9 units to the left, and shift upward 8 units

Answer 1

f(x) = (1/13)|x+9|+8

shifts original f(x) up 8 and left 9 units

and compresses vertically by factor of 13

which is same as stretching horizontally by factor of 13

Answer 2

Begin with the original function.

f(x) = |x|

Shrink vertically by a factor of 13,

f(x) = (1/13) |x|

Shift 9 unites to the left, means replace each x with x + 9.

f(x) = (1/13) |x + 9|

Shift upward 8 units means increase each y value by 8 units.

f(x) = (1/13) |x + 9| + 8

The original graph looks like a V with vertex at (0,0). The shrink vertically squishes it down so it has the same vertex but the branches are more flat. Shift 9 units left and up 8 units puts the vertex at (-9,8).