1.) Explain how the vertical-line test identifies a graph of a function.?

Question

2.) Given a value for f(x), how would you find x?

Answer 1

1. If you pass a vertical line down the graph, and it only passes through the function once, then ya, it is function. If it passes through more than once, then it is not a function.

2. Isolate x

Answer 2

Something is a function if f(x) is uniquely defined for all x in the domain. Uniquely defined means f(x) can't equal two values at the same time - ie, any vertical line cuts the graph at most once.

It really depends on the question - if you just mean from a graph, just look up where the graph hits the value for f(x), and read off x off the axis. But for algebraic ways, it really depends.

Answer 3

Part of being a function is that there's only one value of a given x.

You can't have

f(x0) = y1 and f(x0) = y2 two values for one input.

A vertical line would detect such an occurence because a vertical line has the same x value, if it intersects a curve in more than one place then the curve is not a function.

Answer 4

if you do the vertical line test it can tell of it is function when the line has two points touching at the same time when the vertical line test passes the graph, so if you have a line shaped as a heart, that would not be function

Answer 5

If it is to be a function, any vertical line in the graph can only pass through f(x) once.

Answer 6

1. If f(x) is a function then if f(x) exists at x = a then f(a) is unique

ie any input will at most give one output

So f(x) = tan x is a function

However

x = tan(f(x)) is not a function as this is multivalued for any value of x

So to overcome this a portion of this realation is used namely the range -π/2 < f(x) < π/2 and then the relation becomes the function

f(x) = arctan x

2. You need to solve f(x) = that given value

Answer 7

If a veritcal line touches two or more points, then it is not a function.