FUNCTION OR NOT FUNCTION
1. 3x+y= 4
FUNCTION
- The rule 3x+y= 4 is a function because if y can be expressed in terms of x , anf there is only one value of y for one value of x.
- If x = 1 , then substitute in thr equation, then the value of y would be;
3x+y= 4
[tex]3(1) + y = 4[/tex]
[tex]3 + y = 4[/tex]
[tex]3 - 3 + y = 4 - 3[/tex]
[tex]y = 1[/tex]
2. x²+y²= 4
Not Function
Solution
The relation is not a funtion because if y can be expressed in terms of x, abd there is more than one value of y for one value of x.
[tex]x {}^{\red2} +\red y {}^{\red2} \red - \red4 \\ [/tex]
[tex] {x}^{\red2} \red+ y \red+ x {}^{\red2} = \red4( \red- x {)}^{\red2} [/tex]
[tex]y {}^{\red2} = \red4 \red- x {}^{\red2} [/tex]
[tex]y = \red± \sqrt{\red4 \red- \red2 {}^{\red2} } [/tex]
Notice that for every value of x, there are two values of y,Find th value of y if x=0
[tex]y = \green± \sqrt{\green4 \green- x {}^{\green2} } [/tex]
[tex]y = \green± \sqrt{\green4 \green- \green0 {}^{\green2} } [/tex]
[tex]y = \green± \sqrt{\green4} [/tex]
[tex]y = \green±\green2[/tex]
