Functions and sequences
Evaluate and compose functions, and find terms, ratios and formulas for arithmetic and geometric sequences.
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Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
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About Functions and sequences
A function takes an input and gives exactly one output. f(x) = 2x + 1 means "double it, then add 1", so f(3) = 7. Composing two functions means feeding the output of one into the other.
Sequences are functions on the counting numbers. In an arithmetic sequence you add the same amount each time; in a geometric sequence you multiply by the same amount each time.
Keep in mind
- To evaluate f(a), put a in for every x.
- f(g(x)): work out g first, then put the result into f.
- Arithmetic: aₙ = a₁ + (n − 1)d, where d is the common difference.
- Geometric: aₙ = a₁ × rⁿ⁻¹, where r is the common ratio.
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