4-4.3 Identifying Continuous and Discrete Graphs – Some graphs need to consist of only isolated points instead of being connected. This is determined by the independent variable. If you can have partial amounts of the variable then the graph would be continuous, but if you have to have a whole number of those items then it would have to be discrete to eliminate the in between values. Examples: Continuous or discrete The graph of the amount of water in a pool over the time you are filling it Continuous because you can – measure parts of a minute The cost of basketball tickets to get into a game Discrete because you cannot buy a half of a ticket – 4-4.4 Graphing Non-Linear functions – When the function has an exponent or an absolute value in it then the graph will be non-linear. Luckily, these all have a specific type of graph that goes with them. If the exponent is even then the graph will look like a U shape If the exponent is odd and then it is a U with ½ of it turned the other way If it has an absolute value then the graph is a V shape You have to plot/find enough points to show the change in the graph and show the shape. Examples: X Y X Y X Y 1 2 1 2 1 2 2 1 2 9 2 5 0 3 0 1 0 1 4 1 -1 0 -1 2 5 2 -2 -7 -2 5 If the term with the variable is negative then the U or V shape would just be upside down.
4-4.3 – Identifying Continuous and Discrete Graphs Some graphs need to consist of only isolated points instead of being connected. This is determined by the independent variable. If you can have partial amounts of the variable then the graph would be continuous, but if you have to have a whole number of those items then it would have to be discrete to eliminate the in between values. Examples: Continuous or discrete The graph of the amount of water in a pool over the time you are filling it – Continuous because you can measure parts of a minute The cost of basketball tickets to get into a game – Discrete because you cannot buy a half of a ticket 4-4.4 – Graphing Non-Linear functions When the function has an exponent or an absolute value in it then the graph will be non-linear. Luckily, these all have a specific type of graph that goes with them. If the exponent is even then the graph will look like a U shape If the exponent is odd and then it is a U with ½ of it turned the other way If it has an absolute value then the graph is a V shape You have to plot/find enough points to show the change in the graph and show the shape. Examples: X Y 1 2 2 9 0 1 -1 0 -2 -7 X Y 1 2 2 1 0 3 4 1 5 2 X Y 1 2 2 5 0 1 -1 2 -2 5 If the term with the variable is negative then the U or V shape would just be upside down.