Question

I am so lost. can someone help?? the question is in the picture.

Answer 1

We are given the following function:

`f(x)=x^2`

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:

`h(x)=f(x)-n`

And, to shift a function "m" units to the left we use the following rule:

`h(x)=f(x+m)`

Applying both rules simultaneously we get:

`h(x)=(x+77)^2-5`

2. Reflect about the y-axis.

The rule to reflect a function about the y-axis is the following:

`r(x)=h(-x)`

The means that we will change "x" for "-x" in the function we are going to reflect. Applying the rule we get:

`r(x)=(-x+77)^2-5`

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:

`g(x)=(1)/(m)r(x)`

Applying the rule we get:

`g(x)=(1)/(2)((-x+77)^2-5)`

And thus we get to the final function.