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

$f(4)=4^{2}=16$

$16\neq0$

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

$f(1)=1^{2}=1$

$1\neq-3$

The statement case D is False