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AxiOstra.
MATHEMATICS / START HERE

From a table to your first function.

No knowledge of functions or graphs is needed. Start with one calculation rule, y=2x+1. Follow the numbers into a coordinate system, and discover what the line represents.

Start with a rule and a table

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In y=2x+1, choose a number for x, multiply it by 2, then add 1 to get y. Try the five inputs below. The two numbers in a row belong together.

Multiply by 2. Then add 1.

input x−2after ×2−4output y−3× 2+ 1
x=−2,y=2×(−2)+1=−3x=-2,\qquad y=2\times (-2)+1=-3

x is the number we put in. y is the result after following the rule. The table records both numbers together, one row for each input.

01

Put x=−2 into the rule: 2 × (−2) + 1 = −3. So the row records x=−2 and y=−3. These are an input and its corresponding output.

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One example throughout: y=2x+1, with any real input x. The table contains five examples, and the coordinate window displays only part of the complete line.