Problem 2 will challenge students. The assessment includes a lot of graphs so that students are motivated to consider shortcuts for creating graphs and writing piecewise functions to match the graphs. If you choose to use this resource, you can ask students to write function rules for each of the graphs they create using either absolute value functions or piecewise functions.
Therefore, the piecewise function is: You may also be asked to take an absolute value graph and write it as a piecewise function: We have to start at 0, since dogs have to weigh over 0 pounds: We learned how about Parent Functions and their Transformations here in the Parent Graphs and Transformations section.
The questions also show different transformations of the function. Write a function that models this situation. I will use this information to decide which resource to use in the investigation.
The piecewise function is: Put in numbers and try it! Welcome to She Loves Math!
The level of student of understanding of absolute value functions I observed in the opening determines the flow of the Investigation. Piecewise Function Word Problems Problem: Here are more examples, with explanations.
When they make this connection, they will be able to reason about and visualize absolute value functions more efficiently MP7. It can be helpful to have a reference poster showing a sample problem about continuity on the board, so if there is a student who is interested in making one of these posters, they can use this as a piece of portfolio evidence at the end of the unit.
I am particularly interested in whether students are more engaged in Problem 2 or Problem 3. You plan to sell She Love Math t-shirts as a fundraiser.
Problem 1 will likely require students to get out some notes or reference materials, so if they struggle to start, ask them: A dialogue might proceed as follows: Here are the graphs, with explanations on how to derive their piecewise equations: Look for and make use of structure.
And, even better, a site that covers math topics from before kindergarten through high school. Learn these rules, and practice, practice, practice! To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph.
Graphing Absolute Value Functions Example.
Eventually, I expect students to "invent" or use the idea of a vertex for the absolute value function. So the whole piecewise function is: Obtaining Equations from Piecewise Function Graphs You may be asked to write a piecewise function, given a graph.Determine where the graph is positive vs.
Substitute values into the argument to see if the outcome is positive or negative. Algebra Examples. Step-by-Step Examples. Algebra. Absolute Value Expressions and Equations.
Write the Absolute Value as Piecewise. The piecewise polynomials are when and when. Remove parentheses. Simplify the right side of the equation.
Tap for more steps Divide by. Home Algebra II Linear Equations and Functions Absolute Value Functions. using the symmetry of absolute value functions to our advantage. We know (5, 3) is one point to the right of the vertex; if we go one point to the left of the vertex, Write an equation of the graph shown.
The vertex is (0, 3). This means the beginning of the. Piecewise Functions A Function Can be in Pieces. We can create functions that behave differently based on the input (x) value. A function made up of 3 pieces. Section Lines, Circles and Piecewise Functions. We’re not really going to do any graphing in this section.
In fact, this section is here only to acknowledge that we’ve already looked at these equations and functions in the previous chapter. To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph.
Here are the graphs, with explanations on how to derive their piecewise equations: Absolute Value as a Piecewise Function.Download