Answer:
The correct options are 1,2 and 3.
Step by step explanation:
According to the definition of function there exist unique value of y for each value of x in the domain of the function.
If equation have more than one values of y for any value of x, then the equation is not a function.
[tex]2+x-x^2=14[/tex] .... (1)
[tex]x^2-x-10=24[/tex] ... (2)
A quadratic equation have two values of x and the value of y can be any number. So a quadratic equation is not a function.
The first and second equations are quadratic equations so the equation (1) and (2) are not functions.
The third equation is
[tex]y^2+3x=6[/tex]
The degree of y is 2. It means for each value of x there exist two values of y.
Put x=0, then we get
[tex]y=\pm \sqrt{6}[/tex]
More than one values of y exist for single value of x.
So the equation (3) is not a function.
The fourth equation is
[tex]2y+3x=6[/tex]
Since the degree of x is 1 and degree of y is also 1, therefore it is a linear equation and for each value of x there exist a unique value of y.
Therefore the equation (4) is a function.
