Common Core Math
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Learning Goal

Part of: Construct and compare linear, quadratic, and exponential models and solve problems — 2 of 7 cluster items

Prove growth properties of functions

HSF.LE.A.1.a

**HSF.LE.A.1.a**: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

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HSF.LE.A.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

What you'll learn

  1. Prove algebraically that for f(x) = mx + b, the difference f(x + d) - f(x) = md for any equal spacing d, showing the result is independent of x
  2. Prove algebraically that for g(x) = a * b^x, the ratio g(x + d) / g(x) = b^d for any equal spacing d, showing the result is independent of x
  3. Explain why the constant difference property is equivalent to a constant rate of change (slope)
  4. Explain why the constant ratio property is equivalent to a constant growth/decay factor (base)
  5. Use the proofs to determine whether a given function is linear or exponential without relying solely on tables of values
  6. Connect the algebraic proofs to numerical examples by verifying the formulas with specific values of x and d

Slides

Interactive presentations perfect for visual learners • In development

Slides

In development

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