Math basics › Functions and graphs
What a function is
One input, one output
A function gives exactly one y for each x. That is the whole definition.
The vertical line test
If any vertical line crosses the graph twice, it is not a function. A circle fails this.
Domain and range
Domain is the x values allowed, range is the y values that come out. Watch for division by zero, even roots of negatives, and logs of anything not positive.
f(x) is not multiplication
f(3) means “put 3 in”, not “f times 3”.