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Home > CCA > Chapter 11 > Lesson 11.1.1 > Problem 11-10

11-10.

Given the function $f(x)=x^2−3$ , find the new expression for each part below and describe the transformation.

$f(x)+2$
Hint (a):
Substitute $x^2−3$ for $f(x)$ , then simplify.
Answer (a):
$x^2−1$
Shifted up two units.

$2·f(x)$
Hint (b):
See the help for part (a).
Answer (b):
$2x^2−6$

$f(x+2)$
Hint (c):
Substitute $x+2$ for $x$
in $x^2−3$ , then simplify.
Answer (c):
$f(x)=x^2−3$
$f(x+2)=(x+2)^2−3$
$x^2+4x+1$
Shifted left $2$ units.

$f(2x)$
Answer (d):
$4x^2−3$

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