We have the function:
[tex]f(x)=14x^3-7x^2+6.[/tex]
We must identify the function that:
0. reflects the function across the y-axis,
,
1. shift it 6 units up.
1) To reflect the function across the y-axis we replace x by -x:
[tex]f(x)\rightarrow g(x)=14(-x)^3-7(-x)^2+6=-14x^3-7x^2+6.[/tex]
2) To shift the result 6 units up, we sum +6 on the right side:
[tex]g(x)\rightarrow h(x)=-14x^3-7x^2+6+6=-14x^3-7x^2+12.[/tex]
Plotting both functions, we get:
Answer
Second option
[tex]h(x)=-14x^3-7x^2+12[/tex]
