Step by step
The question
Question: is x² + y² = 25 a function?
x2 + y2 = 25
A function is a rule where each x has only one y.
One x in, one y out.
function: each x has only one y
1 Draw the graph
Draw the grid.
Draw x² + y² = 25.
It is a circle around (0, 0), with radius 5.
2 Vertical line test
The vertical line test: draw straight up-and-down lines.
If one of them hits the graph two times, one x has two y's.
Then it is not a function.
Here is a vertical line at x = 3.
It hits the graph two times!
a vertical line with 2 hits → not a function
3 Read the answer
One vertical line hits it more than once.
So it is not a function.
= no, not a function
4 Check
Let's check with numbers.
x = 3: 3 squared is 9, so y squared is 16.
So y is 4 or minus 4.
Two y's, as the line showed.
The same answer!
x = 3: 9 + y2 = 25 → y2 = 16 → y = 4 or y = −4
Let's look back.
First: draw the graph.
Then: vertical line test.
Then: read the answer.
Last: check.
Answer
= no, not a function