Question

f(x) = x²+5x-1 is shifted 3 units right. The result is g(x). What is g(x)?

Answer 1

In general, given a function h(x), a horizontal shift of h(x) is given by the transformation below

$\begin{gathered} h(x)\rightarrow h(x-a) \\ a>0\rightarrow\text{ a units to the right} \\ a<0\rightarrow\text{ a units to the left} \end{gathered}$

Then, in our case,

$g(x)=f(x-3)=(x-3)^2+5(x-3)-1$

Simplifying,

$\begin{gathered} \Rightarrow g(x)=(x^2-6x+9)+5x-15-1=x^2-x-7 \\ \Rightarrow g(x)=x^2-x-7 \end{gathered}$

Therefore, the answer is g(x)=x^2-x-7