# Lesson 7

Expressing Transformations of Functions Algebraically

### Lesson Narrative

The goal of this lesson is for students to start from an expression of a familiar function and write expressions for transformation of the function from descriptions of the graphical transformation. These transformations include translations and reflections, and require students to focus on what each part of the expression tells them about the corresponding graph (MP7). Students also return to a data set from an earlier lesson to write an equation for a function that models the data, starting from an equation of a function whose graph has the correct shape. In the following lessons, students continue this work of fitting a function to data and learn to adjust the shape of the graph using multiplication.

### Learning Goals

Teacher Facing

• Create equations to represent known translations and reflections of a graph.
• Identify a transformation needed to fit a function to data and represent the new function with an equation.

### Student Facing

• Let’s express transformed functions algebraically.

### Required Preparation

Provide access to graphing technology. If using the print version, students should have access to tracing paper to trace and translate the function.

Be prepared to display the data and graphs for all to see using the embedded applet or other graphing technology.

### Student Facing

• I can write an equation from a description of how a graph is transformed.

### CCSS Standards

A function $$f$$ that satisfies the condition $$f(x) = f(\text-x)$$ for all inputs $$x$$. You can tell an even function from its graph: Its graph is symmetric about the $$y$$-axis.
A function $$f$$ that satisfies $$f(x) = \text-f(\text-x)$$ for all inputs $$x$$. You can tell an odd function from its graph: Its graph is taken to itself when you reflect it across both the $$x$$- and $$y$$-axes. This can also be seen as a 180$$^\circ$$ rotation about the origin.