precal question

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 1/8, shift to the left 5 units, and shift upward 4 units

Answer 1

To shrink vertically by a factor of 1/8, multiply by 1/8 OUTSIDE the absolute value symbols:

f(x)=1/8|x|

To shift to the left by 5 units, add 5 INSIDE the absolute value symbols:

f(x)=1/8|x+5|

To shift upward 4 units, add 4 OUTSIDE the absolute value symbols:

f(x)=1/8|x+5|+4