AP Precalculus · Unit 2: Exponential and Logarithmic Functions · Lesson 2.2

Guided Practice: Change in Linear and Exponential Functions

🧭 Guided Practice
Pick an essential knowledge statement, then step through worked examples one move at a time.
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2.2.A.1Concept

Linear functions of the form f(x) = b + mx are similar to arithmetic sequences of the form an = a0 + dn, as both can be expressed as an initial value (b or a0) plus repeated addition of a constant rate of change, the slope (m or d).

ExampleMatch the sequence to its function1 / 3

The arithmetic sequence an = 5 + 3n has a matching linear function f(x) = 5 + 3x. Identify the initial value and the constant rate of change, then find a2, f(2), and f(2.5).

01234505101520xf(x)

Try it on paper first, then reveal each step to check your work.

Step 1 — Compare the forms
an = a0 + dn matches f(x) = b + mx. So the initial value is 5 (a0 = b = 5) and the constant rate of change is 3 (d = m = 3).
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