College Algebra

Question

if ƒ = ∫(2,3),(-4,4),(5,0),(-3,-4)∫ and g = ∫(pie,3),(-2,0),(0,-4) find the following 1. ƒ(2)             2. ƒ(5)+g(-2)

Answer 1

Remember that y = f(x), so which ordered pair in f has an x = 2?  Answer: (2,3).  So f(2) = y = 3.

 

f(5) = 0   (ordered pair 5,0))

g(-2) = 0  (ordered pair (-2,0))

 

f(5) + g(-2) = 0 + 0 = 0

 

BTW, it's pi, not pie.  ;-)

Answer 2

Hi Kerry,

 

With an ordered pair like (2,3), the x-coordinate is 2.  The y-coordinate is 3.  

The "function notation" f(x) is asking you for the y-value when x is plugged in.  

Any ordered pair could be written as (x,y), but using function notation, this would be written as (x, f(x0).

f(x) is just a y-value.  At our high school, our Algebra 1 teachers have their students cross off every "f(x)" and replace it with "y".

 

Here, with the point (2,3), f(2)=3   <--  notice the "f(...)" is the y-coordinate of the point.  The 2 is the x-coordinate of the point.

 

Notice in the ordered pairs for the set of f, there is only one ordered pair with x=2.  So f(2) is the y-coordinate of the only point in the set with x=2.  And f(2) = 3

 

To find f(5), look for the ordered pair in the set of f that has an x-value of 5.   It is the point (5,0) so f(5) = 0

To find g(-2), look for the ordered pair in the set of g that has an x-value of -2.   This is the point (-2,0), so g(-2) = 0

Now add these to get f(5) + g(-2) = 0 +0 = 0