For each of the following, determine whether the equation defines y as a function of x.

Question

x^2+|y|=1

x=7÷y

9|x|+y=7

3x=y^2

Answer 1

The easiest way is to graph them and see if they pass the Vertical Line Test. If you can draw as vertical line through the graph and cross the graph more than once, it is NOT a function (there are 2 Ys for an X value).

x² + |y| = 1

if you graph this,you can see that if x is 0, y is 1 AND -1

this is NOT a function

x=7÷y by graphing no x can be more than 1 y

this IS a function

9|x|+y=7

by graphing no x can be more than 1 y

this IS a function

3x=y^2

if you graph this,you can see that if x is 12, y is 6 AND -6

this is NOT a function

Answer 2

Is y a function of x?

1. x² + |y| = 1
2. x = 7/y
3. 9|x| + y = 7
4. 3x = y²

Solve each equation for the value of y:

1. x² + |y| = 1

|y| = - x²+1

y is NOT a function of x because any value of x can result in more than one value of y due to its absolute value

2. x = 7/y

y=7/x

y IS a function of x because any x value results in only one value for y

3. 9|x| + y = 7

y = -9|x| + 7

y IS a function of x because any x value results in only one value for y

4. 3x = y²

y² = 3x

y is NOT a function of x because any x value can result in more than one value for y due to the square of its value