Question

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

Answer 1

C and D

Explanation:

`f(x)=\left\{\begin{array}{ccc}-3x,&x<0\\4,&x=0\\x^2,&x>0\end{array}\right\\\\\\A.\ f(1)=-3\\\\1>0\to f(x)=x^2\\\\f(1)=1^2=1\\eq-3\\--------------\\B.\ f(4)=0\\\\0=0\to f(x)=4\\\\f(0)=4\\eq0\\--------------\\C.\ f(3)=9\\\\3>0\to f(x)=x^2\\\\f(3)=3^2=9\qquad\boxed{CORRECT :)}\\--------------\\D.\ f(2)=4\\\\2>0\to f(x)=x^2\\\\f(2)=2^2=4\qquad\boxed{CORRECT :)}`

Answer 2

The statement that is true for the piece-wise function is:

C. f(3)=9

and D. f(2)=4

Explanation:

We are given a function f(x) as:

f(x)= -3x when x<0

4 when x=0

and x² when x>0

Now in order to calculate the value f(1), f(2), f(3), f(4) we need to use the function f(x)= x²

( Since, 1,2,3 and 4 is greater than 0

since the function f(x)=x² is defined for x>0 )

Hence,

we have;

f(1)=(1)²=1

f(2)=(2)²=4

f(3)=(3)²=9

and f(4)=(4)²=16

The correct options are:

Option: C and option: D