Which of the following expressions represents a function? x2 + y2 = 9 {(4, 2), (4, –2), (9, 3), (9, –3)} x = 4 2x + y = 5

Expression 1: 

x² + y² = 9 

It is not a function since, for every value of 'x', there will two values of 'y'

Expression 2:

Here we have four different coordinates [4, 2], [4, -2], [9,3], [9, -3] 
Notice that for the value of x = 4, there are two values of y; 2 and -2
This expression is not a function

Expression 3:

The expression is not a function as it doesn't map the expression onto any value of 'y'

Expression 4:

This expression is a function since, for every value of x, there will be one value of y

A function should pass the vertical line test.

The figure that is shown below that only 2x + y  = 5 satisfies the vertical line test

The expression x² + y² = 9
is a circle, with center at the origin, and with a radius of 3.
It fails the vertical line test.

The data set {(4,2), (4,-2), (9,3), (9,-3)} fails the vertical line test.

The expression x=4 fails the vertical line test.

The expression 2x + y = 5 may be written as
y = - 2x + 5.
It is a straight line which passes the vertical line test.

The expression 2x + y = 5 represents a  function.

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