Let's use this graph:



a. f(2)

This says:  Find 2 on the x axis.  Then go vertically from there
to the graph, and give the value of y there.  The value of y there
is -3.  The point there is (2,-3).  So you write this:

f(2) = -3
 
-------------------------------

 b. f(–4)

This says:  Find -4 on the x axis.  Then go vertically from there
to the graph, and give the value of y there.  The value of y there
is 2.  The point there is (-4,2). So you write this:

f(-4) = 2

-------------------------------
 
c. All x such that f(x) = 0 

This asks in reverse what the other two asked.  They gave you a value
of x and asked for the corresponding value for y.   This gives you a value
of y and asked for the corresponding value(s) for x.

So you look along the graph and find where the graph has a y value of 0,
and give the x values that correspond to a y of zero.

You will see three such points on the graph.  They are (-5.5,0), (-2,0), (3,0), 
 So you write:

f(-5.5) = 0,   f(-2) = 0,   and f(3) = 0

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

It's nothing hard at all, as there is nothing to calculate.
It's just a matter of looking and seeing.  They're just wanting
you to learn functional notation.

f(2) = -3 merely says "The graph contains the point (2,-3)."

f(-4) = 2 merely says "The graph contains the point (-4,2)."

f(3) = 0 merely says "The graph contains the point (3,0)."

f(-2) = 0 merely says "The graph contains the point (-2,0)."

f(-5.5) = 0 merely says "The graph contains the point (-5.5,0)."

"f(x)" means the same thing as "y".


Edwin

Let's use this graph:



a. f(2)

This says:  Find 2 on the x axis.  Then go vertically from there
to the graph, and give the value of y there.  The value of y there
is -3.  The point there is (2,-3).  So you write this:

f(2) = -3
 
-------------------------------

 b. f(–4)

This says:  Find -4 on the x axis.  Then go vertically from there
to the graph, and give the value of y there.  The value of y there
is 2.  The point there is (-4,2). So you write this:

f(-4) = 2

-------------------------------
 
c. All x such that f(x) = 0 

This asks in reverse what the other two asked.  They gave you a value
of x and asked for the corresponding value for y.   This gives you a value
of y and asked for the corresponding value(s) for x.

So you look along the graph and find where the graph has a y value of 0,
and give the x values that correspond to a y of zero.

You will see three such points on the graph.  They are (-5.5,0), (-2,0), (3,0), 
 So you write:

f(-5.5) = 0,   f(-2) = 0,   and f(3) = 0

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

It's nothing hard at all, as there is nothing to calculate.
It's just a matter of looking and seeing.  They're just wanting
you to learn functional notation.

f(2) = -3 merely says "The graph contains the point (2,-3)."

f(-4) = 2 merely says "The graph contains the point (-4,2)."

f(3) = 0 merely says "The graph contains the point (3,0)."

f(-2) = 0 merely says "The graph contains the point (-2,0)."

f(-5.5) = 0 merely says "The graph contains the point (-5.5,0)."

"f(x)" means the same thing as "y".


Edwin