Question

The topic is piecewise functions, can someone help? i’m a little confused :)

Answer 1

Given:

The piecewise function is:

$f(x)=\begin{cases}x+5&x$

To find:

The values of $f(-4),f(-2),f(0),f(3)$.

Solution:

For $x$, the function is

$f(x)=x+5$

For $x\geq -2$, the function is

$f(x)=x^2+2x+3$

a) The value of $f(-4)$ is:

$f(-4)=-4+5$

$f(-4)=1$

b) The value of $f(-2)$ is:

$f(-2)=(-2)^2+2(-2)+3$

$f(-2)=4-4+3$

$f(-2)=3$

c) The value of $f(0)$ is:

$f(0)=(0)^2+2(0)+3$

$f(0)=0-0+3$

$f(0)=3$

d) The value of $f(3)$ is:

$f(3)=(3)^2+2(3)+3$

$f(3)=9+6+3$

$f(3)=18$

Therefore, the required values are $f(-4)=1,f(-2)=3,f(0)=3,f(3)=18$.