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Chapter 31.10
Finding an exponential function given its graph
What You'll Learn
Identify key features of exponential graphs including asymptotes and intercepts
Determine the values of parameters a, b, h, and k from graph information
Apply transformations like reflections and vertical translations to exponential functions
Use coordinate points to set up and solve exponential equations
Verify exponential functions by matching base exponents
What You'll Practice
1
Finding equations in the form y = a·bˣ using two points from a graph
2
Determining exponential functions in transformation form y = 3^(x-h) + k
3
Working with reflected exponential graphs and negative coefficients
4
Solving for unknown parameters using intercepts and asymptotes
Why This Matters
Finding exponential functions from graphs builds your ability to reverse-engineer real-world data patterns. This skill is essential for modeling population growth, compound interest, radioactive decay, and analyzing scientific data where you need to create formulas from observed trends.
This Unit Includes
3 Video lessons
Learning resources
Skills
Exponential Functions
Graph Analysis
Transformations
Asymptotes
Intercepts
Function Notation
Solving Equations
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