Question

Let $f\left(x\right)=x^2+10x+2$. If $g\left(x\right)$ is a transformation that moves $f\left(x\right)$ both one unit up and one unit to the right, then $g\left(x\right)=$

• A. $x^2+8x-6$
• B. $x^2+9x+3$
• C. $x^2+10x-6$
• D. $x^2+11x+3$
• E. $x^2+12+6$

Answer 1

The correct option is A $x^2+8x-6$

The function $g\left(x\right)$ is the transformation that moves $f\left(x\right)=x^2+10x+2$ one unit up and one unit to the right. To move one unit up, add $1$ to the entire function.

And to move one unit to the right, substitute $x=(x-1)$ in the function.

Thus $g\left(x\right)=f(x-1)+1$.

Thus, you need to substitute $x=(x-1)$ throughout the $f\left(x\right)$ and to add $1$ to $f\left(x\right)$: $g\left(x\right)=(x-1{)}^2+10(x-1)+2+1$

$=(x–1)(x–1)+10(x–1)+2+1$

$=x^2-2x+1+10x-10+2+1$

$=x^2+8x-6$