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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
A. Exponential and Logarithmic Functions
8. 12AF.A2.4
8.1 Finding an exponential function given its graph
Finding an Exponential Function from a Graph
Turn a curve on a graph into an equation of the form y equals a times b to the x, using the y-intercept and one other point.
What You'll Learn
Every exponential function can be written as y equals a times b to the x, where a is the y-intercept and b is the growth or decay factor.
Read the y-intercept directly off the graph to find a, since that is the value when x equals 0.
Pick a second clear point on the curve and substitute it into the equation to solve for b.
A base greater than 1 means growth and a base between 0 and 1 means decay, which you can confirm from the shape of the curve.
When the y-intercept is not shown, use two known points and divide one equation by the other to solve for b first.
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
ON Curriculum Aligned