Hey there! Ready to explore how math helps us see patterns in the real world? Let's dive into the awesome world of functions and graphs together!
A function is like a magical math machine. You slide an 'input' number in, the machine applies a specific rule, and it pops out exactly one 'output' number.
We often call the input 'x' and the output 'y'. If our rule is 'add 2', then putting in 3 gives us 5. We can write this relation as an ordered pair: (3, 5).
When we plot these input-output pairs on a coordinate grid as points (x, y), they form a graph. If the points form a straight line, we call it a linear function!
✏️ Worked example
If our function rule is y = 2x - 1, find the output (y) when the input (x) is 3, and write it as an ordered pair.
Identify the given function rule: y = 2x - 1.
Replace the variable 'x' with the input value of 3: y = 2(3) - 1.
Multiply 2 by 3 to get 6: y = 6 - 1.
Subtract 1 to find the final output: y = 5.
Combine the input (3) and output (5) into the ordered pair: (3, 5).
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