In this lesson, students will learn how to find the input and output of a function. Students will start by evaluating expressions. From there, they will learn about inputs and outputs with equations and tables. Then, students will see how graphs can be used to find the input or output. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students will be able to find the input and output of a function.
Students should review how to evaluate expressions when given a value for the variable. Once students have the expressions simplified, they should compare with a partner. This warm up can help you identify students that may struggle with integer operations.
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When reviewing with students, make sure they are able to explain how they arrived at their respective answers. Once the expressions have all been simplified, add “`y =`” in front of each expression. Ask students if this would affect their answers or change how they would evaluate the expressions. Once students recognize that the evaluated expression represents the `y`, ask students what would happen if you changed `x`, or the input. Students should recognize that their final answer changes based on the value they plug in.
Because students have already evaluated when `x = -2`, using `y = 2x + 1`, have students try to fill in the rest of the table shown. Consider asking students which variable represents the input, and which variable represents the output and how they know. To scaffold more, only have students fill in the two missing `y`-values first. From there, provide support to help them better understand what to do when given the output.
Students will likely not have issues when plugging in new inputs. When plugging in outputs though, students may accidentally still plug in the `y`-values for `x` instead. Remind students to be mindful of where they plug in values, and encourage them to use the vocabulary when finding the input and output of a function. Students should be able to explain how to solve the equation, but you can provide additional support if needed.
To help solidify students’ understanding, give students some time to attempt these problems. Students can check their work with a partner to compare and catch any minor misconceptions, such as integer operations.
Students may struggle with the fraction coefficient in the equation, which gives you an opportunity to review multiplying fractions and whole numbers if needed. For the table, students may need a reminder to plug in the given values where they belong.
Because of students’ familiarity with the equation `y = 2x + 1` at this point, use the table students created earlier to graph the points. It may help if you explicitly let students know they had already filled in the table.
Ask students to relate the ordered pairs of the points to input and output. Although students were able to use the table to make the graph, ask students how they would find the inputs and outputs of the function if they were only given the graph.
There are two separate examples for finding the input and output of a function given a graph. The first example is a linear function, while the second is a nonlinear function. Students should identify the corresponding outputs for each input. If needed, students can make a table to organize their thoughts.
When reviewing, ask students how they differentiate between the input and the output on the graph. It may be helpful to use colors to highlight the axes with input and output. Consider asking students if they would be able to find the input given the output, such as identifying the input when the output is `0` for each graph.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn lets you access tons of practice problems for finding the input and output of a function. Check out the online practice and assign to your students for classwork and/or homework!
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