Answer:
The graph of the functions moves 4 units right, 3 units up stretches vertically by a factor of 3 and reflects horizontally.
Step-by-step explanation:
In order to find the function transformations, we must first determine what the base function is:
[tex]f(x)=x^{2}[/tex]
Next, we need to determine how the function is being affected by the transformations.
When the graph of the function moves 4 units right, we mus subtract 4 units from x, so the function looks like this then:
[tex]f(x)=(x-4)^{2}[/tex]
If we need to stretch it vertically by a factor of 3, we need to multiply the function by 3:
[tex]f(x)=3(x-4)^{2}[/tex]
If we need to reflect it horizontally, then we turn the 3 into a negative so we get:
[tex]f(x)=-3(x-4)^{2}[/tex]
And finally, if we wanted to move the graph up by 3 units, then we need to add 3 units to the whole graph, so we get:
[tex]f(x)=-3(x-4)^{2}+3[/tex]
in the attached picture you will be able to see the graph of the base function with all the transformations.
