Help students master one of the most essential skills in the exponential functions unit — writing y = a · bˣ from a table of values or a graph. This guided notes packet walks students through a clear set of steps for each representation, then builds fluency through four worked examples that cover both growth and decay, with and without the y-intercept given.

What's Included

• Essential Question
• Exponential Function Form (y = a · bˣ with definitions of a and b)
• Steps for Writing from a Table (3 steps)
• Steps for Writing from a Graph (4 steps)
• 4 Worked Examples (2 from tables, 2 from graphs)

Perfect For

• Introducing students to writing exponential functions from multiple representations
• Building procedural fluency alongside conceptual understanding
• Guided instruction and interactive note-taking
• Small group work or whole-class lesson delivery
• Review before assessments on exponential functions

Why Teachers Love This Resource ✓ Steps for tables and graphs are clearly separated so students know exactly which process to apply ✓ Covers both growth and decay, including a table with decimal y-values ✓ Graph examples include one with a visible y-intercept and one without, building full flexibility ✓ Fill-in format keeps students actively engaged during instruction ✓ Clean, organized layout makes it easy to use as a study reference ✓ Pairs naturally with exponential growth and decay lessons ✓ Ready to print and use — no prep required

Student-Friendly Features

• Step-by-step procedures broken into numbered lists for each representation
• Tables and coordinate grids included directly on the notes page
• Consistent y = a · bˣ form reinforced across all four examples
• Decimal values in one table prepare students for real-world data

Skills Developed

• Identifying the common ratio from a table of values
• Finding the initial value when x = 0 is and is not in the table
• Reading the y-intercept from a graph to determine a
• Using two points to find b when x-values differ by more than 1
• Substituting a known point to solve for a
• Writing exponential functions in y = a · bˣ form

Conceptual Emphasis

• Understanding a as the initial value and b as the multiplier connecting consecutive outputs
• Recognizing decay from a ratio between 0 and 1, including decimal bases
• Seeing that the same algebraic structure applies regardless of whether the starting representation is a table or a graph

When to Use After students are comfortable with the form y = a · bˣ and can identify growth vs. decay — this lesson builds the skill of constructing exponential functions from data, bridging evaluation and modeling. Pairs directly with Exponential Growth and Decay guided notes.