SOLUTION: please help me find if these are functions or not -2x+4y=0 x to the second power + y to the second power = 8 IF F(X) = 2X-4 AND G(X) = X TO THE SECOND POWER - 4X, FIND EAC

Algebra ->  Functions -> SOLUTION: please help me find if these are functions or not -2x+4y=0 x to the second power + y to the second power = 8 IF F(X) = 2X-4 AND G(X) = X TO THE SECOND POWER - 4X, FIND EAC      Log On


   



Question 695657: please help me find if these are functions or not
-2x+4y=0
x to the second power + y to the second power = 8
IF F(X) = 2X-4 AND G(X) = X TO THE SECOND POWER - 4X, FIND EACH VALUE.
G(2)
F(-5)
G(-3)
G(2C)
F(3X)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if these are functions or not
first recall definition of a +Function:
A function is a set of ordered pairs in which each x-element has only+ONE+y-element associated with it.
1.
-2x%2B4y=0
graph it first using x and y-intercept
x-intercept: set y=0
-2x%2B4%2A0=0
-2x=0....=>...x=0
y-intercept: set x=0
-2%2A0%2B4y=0
4y=0....=>...y=0

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F2%29+
as you can see, each x-element has only+ONE+y-element associated with it, and -2x%2B4y=0 is a +function
Just remember:
A function may not have two y-values assigned to the same x-value, such as (2,4), (2%2C6).
A function may, however, have two x-values assigned to the same y-value, such as (2,4), (3%2C4).

2.
x%5E2+%2B+y%5E2+=+8.....here you have a circle

is a circle is a function or not , the answer is clearly no, if we use vertical line test
In the Cartesian system, there is no function that whose plot is a circle. In a polar or parametric system functions can readily have circular plots.




3.
if f%28x%29+=+2x-4 AND g%28x%29+=+x%5E2+-+4x, than

G(2)...g%282%29+=+2%5E2+-+4%2A2=4-8=highlight%28-4%29
F(-5)....f%28-5%29+=+2%28-5%29-4=-10-4=highlight%28-14%29
G(-3).......g%28-3%29+=+%28-3%29%5E2+-+4%2A%28-3%29=9%2B12=highlight%2821%29

G(2C)......g%282C%29+=+%282C%29%5E2+-+4%282C%29=highlight%284C%5E2-8C%29
F(3x)........f%283x%29+=+2%283x%29-4=highlight%286x-4%29