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<-2\\x^2+2x+3&x\geq -2\end{cases}`

To find:

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

Solution:

For
`x<-2`, 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`.