Question

Given the piecewise function shown below, select all of the statements that are true. f(x)= {-3x, x<0; 4,x=0; x^2, x>0} A. f(3)=9 B. f(4)=0 C. f(2)=4 D. f(1)= -3

Answer 1

The following statements are true.

f(3) = 9

f(2) = 4

Answer 2

we will proceed to calculate each case to determine the solution of the problem

case A
`f(3)=9`

For
`x=3`

`x > 0`

so

`f(x)=x^(2)`

substitute the value of x

`f(3)=3^(2)=9`

`9=9`

The statement case A is True

case B
`f(4)=0`

For
`x=4`

`x > 0`

so

`f(x)=x^(2)`

substitute the value of x

`f(4)=4^(2)=16`

`16\\eq0`

The statement case B is False

case C
`f(2)=4`

For
`x=2`

`x > 0`

so

`f(x)=x^(2)`

substitute the value of x

`f(2)=2^(2)=4`

`4=4`

The statement case C is True

case D
`f(1)=-3`

For
`x=1`

`x > 0`

so

`f(x)=x^(2)`

substitute the value of x

`f(1)=1^(2)=1`

`1\\eq-3`

The statement case D is False