consider the function given by the graph. what are these values?\n$f(-2)=$\n$f(0)=$\n$f(4)=$

Explanation:

Step1: Find ( f(-2) )

For ( x = - 2 ), look at the graph. The point on the graph when ( x=-2 ) has ( y = 3 ). So ( f(-2)=3 ).

Step2: Find ( f(0) )

For ( x = 0 ), the solid - dot (which represents the value of the function at that point) has ( y = 3 ). So ( f(0)=3 ).

Step3: Find ( f(4) )

For ( x = 4 ), use the second part of the piece - wise function. The line passes through ( (2,0) ) and has a slope ( m=\frac{0 - (-1)}{2-4}=\frac{1}{-2}=-\frac{1}{2} ). The equation of the line using the point - slope form ( y - y_1=m(x - x_1) ) with ( (x_1,y_1)=(2,0) ) is ( y-0=-\frac{1}{2}(x - 2) ), or ( y=-\frac{1}{2}x + 1 ). When ( x = 4 ), ( y=-\frac{1}{2}\times4+1=-2 + 1=-1 ). So ( f(4)=-1 ).

Answer:

( f(-2)=3 ), ( f(0)=3 ), ( f(4)=-1 )