SOLUTION: Evaluate each piecewise function at the given values of the independent variable. a. F(-2) b. F(0) c. F(3) {{{F(x)=system(3x+5,4x+7)}}}{{{matrix(2,1,x<0,x>=0)}}}

F(-2) means the value of y when x = -2.
F(0) means the value of y when x = 0.
F(3) means the value of y when x = 3.

F(x) is defined by:



That means if we want to find F("some number"), we use 3x+5 to find the
y-value if "some number" is less than 0 and we use 4x+7 to find the
y-value if "some number" is equal to 0 or greater than 0. 

Here is the graph of F(x):



Notice that there is an open circle at the point (0,5),
and a closed circle at (0,7).  The graph does not include
the point (0,5) but does include the point (0,7).

--------------------------------------------

a. F(-2) means the value of y when x = -2.  

Since -2 is less than 0, we use 3x+5 to calculate the y-value:

        3x + 5

F(-2) = 3(-2)+5
F(-2) = -6+5
F(-2) = -1

That just means that the point (-2,-1) is on the graph, as you see
plotted below:


 
------------------------------------------------

b. F(0) means the value of y when x = 0.  

Since 0 is equal 0 we use 4x+7 to calculate the y-value:

        4x + 7

F(0) = 4(0)+7
F(0) = 0+7
F(0) = 7

That just means that the point (0,7) is on the graph, which is the
closed circle on the graph:



--------------------------------------------

c. F(3) means the value of y when x = 3.  

Since 3 is greater than 0, we use 4x+7 to calculate the y-value:

       4x + 7

F(3) = 4(3)+7
F(3) = 12+7
F(3) = 19

That just means that the point (3,19) is on the graph, as you see
plotted below:


 
------------------------------------------------
Edwin