Question

$f\left(x\right)=2x^2$ is translated $2$ units to the right and $1$ unit up. If the resulting graph is $g\left(x\right)$, then what is $g\left(3\right)$?

• A. $3$
• B. $11$
• C. $15$
• D. $26$
• E. $31$

Answer 1

The correct option is A $3$

$y=f\left(x\right)$ is translated $2$ units to the right. Hence, $f\left(x\right)$ transforms to $f(x-2)$. Then, it is translated $1$ unit upwards. Hence the new function is $g\left(x\right)=f(x-2)+1$
$\therefore g\left(x\right)=2(x-2{)}^2+1$

$g\left(3\right)=2(3-2{)}^2+1=2+1=3$