Common Graphs To Memorize - UM Math Prep

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Graph basics

There are certain descriptions which are often used when we talk about graphs.

Descriptions of graphs
"The graph is positive" means that the y-values of the graph are positive.
"The graph is negative" means that the y-values of the graph are negative.
"The graph is increasing" means that as we move from left to right the y-values on the graph climb.
"The graph is decreasing" means that as we move from left to right the y-values on the graph drop.
Examples
graph of an increasing positive valued function graph of an decreasing positive valued function
ys are positive (the graph lies above the x-axis) ys are increasing (the graph climbs from left to right) ys are positive (the graph lies above the x-axis) ys are decreasing (the graph drops from left to right)
graph of an increasing positive valued function graph of an decreasing positive valued function
ys are negative (the graph lies below the x-axis) ys are increasing (the graph climbs from left to right) ys are negative (the graph lies below the x-axis) ys are decreasing (the graph drops from left to right)
Be careful not to confuse "the graph is negative" with "the x-values are of the graph are negative" graph of f(x) positive for x 0 Here the x-values are negative, but the graph is positive.

Essential information to memorize about graphs

For each of the graphs below, you should memorize each of the following pieces of information, or should be familiar enough with the graph that you can determine each from your knowledge of the graph.

  • domain
  • range
  • general shape
  • intercepts and key values
  • asymptotes

Common graphs to memorize

graph of y=mx+b graph of y=x^2
y=mx+b y=x^2
graph of y=x^3 graph of y=sqrt(x)
y=x^3 y=sqrt(x)
graph of |x| graph of 1/x
y=|x| y=1/x
graph of x^2+y^2=1 graph of y=ln x
x^2+y^2=1 y=ln x
graph of y=e^x graph of y=e^(-x)
y=e^x y=e^(-x)
graph of y=cos x graph of y=sin x
y=cos x y=sin x
graph of y=tan x
y=tan x
Practice

For practice, go back through the graphs above. We're just memorizing what the different functions look like, so you want to be able to automatically associate the graph with the corresponding function and vice-versa. To test yourself on which function is associated with each graph, scroll down through the graphs being careful to leave the function off the bottom of your browser window. You can scroll upwards to test the reverse association.

home | prev: section next: topic next page precal: 14.1 - graphs to memorize page created: Sat Mar 14 18:19:44 2026 Comments to math-itc(at)umich(dot)edu ©2003-2007 Gavin LaRose, Pat Shure / University of Michigan Math Dept. / Regents of the University of Michigan

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