Question

Which among the following relations between $x,y$ doesn't represent a function

• A. $(x-1{)}^2+(y-3{)}^2=5^2,x\in [-4,6],y\in R$
• B. $y^2=4x,x\in [0,\infty ),y\in R$
• C. $x^2=4y,x,y\in R$
• D. $y=2x+5^2,x,y\in R$

Answer 1

Answer: (A), (B)

$y^2=4x,x\in [0,\infty ),y\in R$

We know that if a vertical line parallel to $y$-axis for the curve cuts the graph at one point, then it represents a function.


Here vertical line cuts the graph at more than one point.
$\therefore$ It is not a function.


Vertical line is cutting the graph at more than one point.
$\therefore$ It is not a function.


Vertical line is cutting the graph at only one point.
$\therefore$ It is a function.


Vertical line is cutting the graph at only one point.
$\therefore$ It is a function.