We are given the function:
[tex]f(x)=\sqrt{x}[/tex]
we are asked to do the following transformations:
Part A.
[tex]g(x)=f(x+4)[/tex]
This is s transformation of the form:
[tex]h(x)=f(x-a)[/tex]
In this case, "a" is a negative number. This is a translation of the graph 4 units to the left since "a" is negative. If "a" were positive then it would be a translation to the right.
To determine the function we substitute the value of "x" in f(x) for "x + 4", like this:
[tex]g(x)=\sqrt{x+4}[/tex]
The graph of the function is:
Part B.
We are given the follwing transformation:
[tex]g(x)=2f(2x-1)[/tex]
The first transformation is to stretch the function by a factor of "2", which means that we change "x" for "2x" in f(x):
[tex]f(2x)=\sqrt{2x}[/tex]
Now, we translate the streched function 0.5 units to the right. That means that we change "2x" for "2x - 1";
[tex]f(2x-1)=\sqrt{2x-1}[/tex]
Now, we multiply the function by 2. This means that the function is stretched by a factor of 2.
[tex]g(x)=2f(2x-1)=2\sqrt{2x-1}[/tex]
The graph of the function is the following:
Part c. In this case, this is the function translated by 1 unit to the right. The graph is the following:
Part D. This is the function translated 1 uni
