Question

I need help with this please help me

Answer 1

The graph is shown below.

Explanation:

The given piecewise function is

`f(x)=\begin{cases}-x & \text{ if } x<0 \\ x^2 & \text{ if } x\geq 0 \end{cases}`

From the given piecewise function, it is clear that

`f(x)=-x` for x<0.

Put different values of x in f(x) where x<0 and find the values of f(x) to make a table of values as shown below.

Table of values:

x f(x)

-3 3

-2 2

-1 1

Now, plot the points (-4,4),(-3,3),(-2,2),(-1,1) and join them by straight line. There is an open circle at x=0 because 0 is not included in this function.

From the given piecewise function, it is clear that

`f(x)=x^2` for
`x\geq 0`.

Table of values:

x f(x)

0 0

1 1

2 4

Plot the points (0,0), (1,1), (2,4) and join them by a curve. There is closed circle at 0 because 0 is included in this function.

The graph is shown below.