This powerpoint contains eight slides that emphasize that functions are represented by graphs but there are also several other representations used to illustrate a function.
The Do Now, the second and third slide, illustrate a function as
• an equation
• a graph
• a set of table values
• a function machine
• a real world description
• a set of ordered pairs
and shows where the domain, range, input, output, x-value, and y-values are located in each representation.
• Slide four begins with an equation with a given domain. It shows an input-output table with only the input values filled in. Students are asked to fill in the output values based on the equation given. Then students are asked to graph the set of input-output values. Students are reminded to observe that every output value is one-third of each input value, just like the equation described. For the given domain a clear picture of five points are lined up on a graph to represent the equation and the inputs and outputs.
• Slide five starts with a new equation and a new domain. The same steps are used to notice the relationship between the equation, the input-output table and the graph. Again, for the given domain, a clear picture of five points lined up on a graph is repeated again.
• Slide six introduces a real world scenario that describes a function. The input values represent the first five days of a week and the output represents the number of hours the average student spends working on homework. The students are presented with the set of table values for this scenario and then asked to complete a graph for the input-output values. Students notice that input values are graphed on the x-axis and the output values are graphed on the y-axis. Students should notice all the illustrated forms of a function shown on the slide: a graph, a set of table value, a real world description, and a set of ordered pairs. No equation is given for this function.
• Slide seven is a second example like slide six.
• On slide eight students are shown a graph of a function. From their experience with slides four and five, students are challenged to try to write an equation that matches the graph. Students might find it helps them to record the input and output values in the table from the graph and then notice the relationship between the two lists. They should notice that each output value is two more than each input value.
• Slide nine is similar to slide eight but the equation is more challenging to discover.
• The final slide in the lesson describes a real world scenario and presents a set of input-output values to fit the real world scenario. Before graphing the table values students are asked to pick out the input and output values by naming the domain and range of the function. Students are asked to make a generalization about what the graph will look like from the table of values. Students should confirm their conjecture by completing the graph.
This powerpoint file can be used to introduce students to the concept that there are many ways to represent a function and that they are all related to each other.
This identical file is available in my store as a Smart Notebook file “Functions Defined By Graphs = SN”