# Obtaining information from the graph of a functional relationship

### Graphs of Functions

Argomenti trattati: function, functions, graph, inverse. in which case the inverse relation is the inverse function: the inverse relation is the relation obtained by. curve on the graph. So how do we find the equation of curve from the graph ( curve on the graph is similar to the graph of the quadratic function)? c is very easy to obtain, it is just the point where your curve intersects the y-axis. b is the . Then, propose a mathematical relationship that governs these variables. Usually . In Section we defined a function as a special type of relation; one in which each The graph of a function f is the set of points which satisfy the equation y = f(x). . Putting all of this information together and plotting additional points, we get.

Thus, a circle is not the graph of a function. Vertical line test We see that we can draw a vertical line, for example the dotted line in the drawing, which cuts the circle more than once. Therefore the circle is not a function. Does this graph pass the vertical line test?

## Functions and Graphs

It passes the vertical line test. Therefore, it is the graph of a function. It does not pass the vertical line test because the vertical line we have drawn cuts the graph twice, so it is not the graph of a function. Definition A one to one function is a function which associates distinct arguments with distinct values; that is, every unique argument produces a unique result.

It is not necessary for all elements in a co-domain to be mapped. And then we get to x is equal to 4, where it seems like this thing that could be a function is somewhat defined.

It does try to associate 4 with things. But what's interesting here is it tries to associate 4 with two different things. All of a sudden in this thing that we think might have been a function, but it looks like it might not be, we don't know.

Do we associate 4 with 5?

### Functions and Graphs

Or do we associate it with negative 1? So this thing right over here is actually a relation. You can have one member of the domain being related to multiple members of the range. But if you do have that, then you're not dealing with a function. So once again, because of this, this is not a function.

It's not clear that when you input 4 into it, should you output 5? Or should you output negative 1? And sometimes there's something called the vertical line test that tells you whether something is a function.

When it's graphically defined like this, you literally say, OK, when x is 4, if I draw a vertical line, do I intersect the function at two places or more? It could be two or more places. And if you do, that means that there's two or more values that are related to that value in the domain.

## Recognizing functions from graph

There's two or more outputs for the input 4. And if there are two or more outputs for that one input, then you're not dealing with a function. You're just dealing with a relation. The approximations -1,4 and 2,-8 are not very close to the real relative extreme points, so we will use the zoom and trace features to improve the approximations.

When you click the Trace button, a point on the graph of f is indicated with a small circle.

The coordinates of that point are reported in the two text boxes near the Trace button. If you select a larger Step Size from the pull down menu, then the trace point moves farther with each click. It is possible to move faster with the enter key than with the mouse. Using the default view, the lowest point found while tracing near the minimum point is 1. Note that this is not the exact location of the minimum point.

We need to look at the trace points on either side of this point to get an idea of how close we are. Find this trace point, make sure that the Step Size is set to 1, and then find the points on either side of this point.