How does a function look like on a graph?

Answer 1

A function can look like almost anything on a graph. It depends what the function is. The only rule is that if you have the graph of a function, any vertical line you draw cannot intersect the graph of the function more than once.

Answer 2

Aside the excellent explanations above, if you forget everything else, just remember to draw a table with one column for x, and other for y. Then choose numbers you want for x (I usually use -2, -1, 0, 1, 2, etc.), write it into the column for x, plug each into equation, write the result into column for y, and draw those points on the graph. Each point is actually a pair of coordinates, determined by the values for x and y: (x1, y1), (x2, y2), ....

Note:
- we are plugging both positive and negative numbers, to make sure we have all bases covered
- a value that would give a solution in the case equation is equal to 0, will intersect with an x-axis (coordinates: x,0). You can find it/them by solving the case when y = 0.
- respect restrictions: a value that would give 0 as a result for denominator, implies that there is an asimptote (infinity line) involved. [E.g. y=1(x-4) Since x-4=0, and x=4, if you choose x=4, for that point you will have an infinite line, since it gives (4, infinity). This will sometimes limit your function to the infinity line; at other times you will have two or more curves getting closer and closer to the infinity line, but never touching or intersecting it.

Answer 3

One arbitrary way of defining what a function looks like on a graph is that is passes the "vertical line test" (explanation below).

The "vertical line test" is such that if you make ANY vertical line on the graph, it only goes through the graph in AT MOST one point. If it goes through more than one point, then it is known as a relation.

A circle, x^2 + y^2 = 25, is not a function, because it fails the vertical line test, and goes through two points at some vertical line.

A parabola, y = x^2 + 5x + 6, is a function; any vertical line will go through at most one point.

Visually, that is one way to determine a function.

Answer 4

There are eight (8) different types of functions. They all look differently. They are listed below with a picture (the link), the basic equation, and what they're called.

Identity function (y=x)
http://www-math.mit.edu/18.013A/HTML/chapter01/images/identity.gif

Absolute value function (y=|x|)
http://library.thinkquest.org/20991/media/alg2_absval.gif

Square function (y=x^2)
http://campus.northpark.edu/math/PreCalculus/Transcendental/Trigonometric/Solving/images/square.gif

Square root function (y= [square root of x])
http://www.richland.edu/james/lecture/m116/functions/sqrt.gif

Reciprocal function (y=1/x)
http://www.gomath.com/htdocs/images/7-10-01(6).gif

Cubic function (y=x^3)
http://www.richland.edu/james/lecture/m116/functions/cubic.gif

Exponential function (y=2^x)
http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/mathgifs/andro2_ss1.gif

Greatest integer function (y=[x])
http://mathforum.org/workshops/sum98/participants/glazer/phone/floor.gif

I hope this helps you a lot!

Answer 5

There are a lot of different kinds of functions, so they all look different. You can't just generalize like that.