Transformations:
- To move upward on a graph the equation would had a number added to the end of it.
- Example: X^2 +3: this would move the graph up 3 units.
- To move downward on a graph the equation would have a number added to the end of it.
- Example: X^2 - 4
- To move right on a graph the equation would have a number subtracted from the X in a parenthesis.
- Example: (X-3)
- To move left of the graph the equation would have a number added to the X in a parenthesis.
- Example: (X+3)
- To reflect across the X-axis on a graph the equation would have a negative in front of the X outside of the parenthesis.
- Example: (X) now becomes -(X)
- To reflect across the Y-axis on a graph the equation would have a negative in front of the X inside of the parenthesis.
- Example: (X) now becomes (-X)
- To compress vertically on a graph the equation would have a number added in front of the X that is greater than 1.
- Example: 7+X
- To stretch vertically on a graph the equation would have a number added in front of the X that is greater than 0 but less than 1.
- Example: 1/2 + X
- To compress horizontally on a graph the equation would have the X multiplied by a number greater than 1.
- Example: (7X)
- To stretch horizontally on a graph the equation would have the X multiplied by a number greater than 0 and less than 1.
- Example: (1/2X)
- To graph a piecewise function, each equation needs to be solved to get a certain set of points.
- There are three different steps to solve which will give you six different sets of points.
- In each step you will need to plug in a value and solve the one step equation.
- The equations consist of a greater than, less than, greater than or equal to, or less than or equal to.
- The equal to inequalities are a closed point of the graph and the original greater than and less than inequalities are an open point on the graph.