We are given the following function:
We are asked to do the following tranformations:
1. Shift down 5 units and left 77 units.
First, to shift a function down a number "n" of units we follow the next rule:
And, to shift a function "m" units to the left we use the following rule:
Applying both rules simultaneously we get:
2. Reflect about the y-axis.
The rule to reflect a function about the y-axis is the following:
The means that we will change "x" for "-x" in the function we are going to reflect. Applying the rule we get:
3. Compress vertically by a factor of 2.
To compress a function vertically by a factor "m" we multiply the entire function by 1/m, like this:
Applying the rule we get:
And thus we get to the final function.
