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

User Yollanda
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1 Answer

10 votes
10 votes

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

User Chrisbedoya
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2.4k points
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