Question

Given the piecewise function shown below select all the statements that are true

Answer 1

The correct options are
`f(-1)=2` and
`f(1)=0`.

Explanation:

We are given the function,

`\left\{\begin{matrix}-x+1&x<0\\-2&x=0\\x^2-1&x>0\end{matrix}\right`.

Now, according to the options, we have,

When x= -1 and x= -2, the function is
`f(x)=-x+1`.

Then,
`f(-1)=-(-1)+1=1+1=2`

Also,
`f(-2)=-(-2)+1=2+1=3`

When x= 1 and x= 4, the function is
`f(x)=x^2-1`

Then,
`f(1)=1^2-1=1-1=0`

Also,
`f(4)=4^2-1=16-1=15`

Thus, the correct options are
`f(-1)=2` and
`f(1)=0`.

Answer 2

The piecewise function tells us specific rules he should execute based on the input x we put in. For example for answer A is true since we use the top function f(x) = -x + 1 since the input is -1 which is less than 0 (x < 0). We check to make sure the equation comes out true:

f(-1) = -(-1) + 1

f(-1) = 2 ✓