### Home > CCA > Chapter 11 > Lesson 11.1.1 > Problem11-10

11-10.

Given the function $f(x)=x^2−3$, find the new expression for each part below and describe the transformation. 11-10 HW eTool (Desmos). Homework Help ✎

1. $f(x)+2$

Substitute $x^2−3$ for $f(x)$, then simplify.

$x^2−1$
Shifted up two units.

1. $2·f(x)$

See the help for part (a).

$2x^2−6$

1. $f(x+2)$

Substitute $x+2$ for $x$
in $x^2−3$, then simplify.

$f(x)=x^2−3$
$f(x+2)=(x+2)^2−3$
$x^2+4x+1$
Shifted left $2$ units.

1. $f(2x)$

$4x^2−3$