Answer:
[tex]y = {x}^{2} + 6[/tex]
Step-by-step explanation:
The given function is
[tex]y = {x}^{2} + 1[/tex]
We want to find a function that shifts this function up by 5 units.
We let:
[tex]f(x) = {x}^{2} + 1[/tex]
Then the transformed function we are looking for is
[tex]g(x) = f(x) + 5[/tex]
This implies that:
[tex]g(x) = {x}^{2} + 1 + 5[/tex]
[tex]g(x) = {x}^{2} + 6[/tex]
Hence the function we are looking for is
[tex]y = {x}^{2} + 6[/tex]
