# Lesson 12

Connections between Graphs and Equations

These materials, when encountered before Algebra 1, Unit 5, Lesson 12 support success in that lesson.

### Lesson Narrative

In the associated Algebra 1 lesson, students examine how the parameters $$a$$ and $$b$$ in a function of the form $$a \boldcdot b^x$$ influence its graph. In order to engage with the lesson, students need to recall that $$a$$ is the value the function takes at 0 and $$b$$ is its growth factor. To prepare for this, in this support lesson, students have opportunities to recall the significance of given parameters in specific linear and exponential functions. They do this through constructing tables for functions defined with a given expression, and then using technology to graph each function and explain where they can see the parameters in the graph. Finally, they create new functions by making strategic modifications to the functions they have been working with. In order to do this, they need to understand how the given functions relate to the context and to their graphs, which is an example of reasoning abstractly and quantitatively (MP2).

### Learning Goals

Teacher Facing

• Practice evaluating functions at different values and interpreting them for a situation.

### Student Facing

• Let’s examine some situations, equations, and graphs.

Building On