How to Graph a Function
Graphs of Functions
The first graph is a linear function. It graphs a line. The second graph is what’s called a quadratic function. Quadratic functions graph a U, or a parabola. The third graph is an exponential function. Exponential functions start out increasing very slowly, then start increasing more and more rapidly.
This next graph is the graph of a logarithmic function. A logarithmic function is the inverse of an exponential function. We should also talk about the asymptote of an exponential and a logarithmic function. An exponential function has a horizontal asymptote of y equals 0, while a logarithmic function, since it’s the inverse of an exponential function, has a vertical asymptote of x equals 0.
An asymptote is just a line that the graph is approaching but doesn’t cross. The next graph is what’s called an absolute value function. It graphs a V. It looks like a V. They’re both straight lines, and the left side is just the reflection of the right side. This next graph is the graph of a square root function.
A square root function is a parabola turned on its side. It’s just the top half of the parabola turned on its side. The last function is the graph—this is the graph of a rational function. Rational functions have two branches, one in the first quadrant and one in the third quadrant.
If you look at this branch here, as we move from left to right it’s decreasing, and the same with the other branches as we move from left to right. It decreases. There are some of the basic functions and their graphs.