Input-Output View Math Example 2

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Example 2

medium
A function machine applies two operations in sequence: first square the input, then add 33. Write the function formula f(x)f(x), fill in a table for x∈{−2,−1,0,1,2}x \in \{-2,-1,0,1,2\}, and identify any symmetry.

Solution

  1. 1
    Translate operations: square then add 33 gives f(x)=x2+3f(x) = x^2 + 3.
  2. 2
    Build table: f(−2)=7,  f(−1)=4,  f(0)=3,  f(1)=4,  f(2)=7f(-2)=7,\; f(-1)=4,\; f(0)=3,\; f(1)=4,\; f(2)=7.
  3. 3
    Symmetry: f(−x)=(−x)2+3=x2+3=f(x)f(-x) = (-x)^2+3 = x^2+3 = f(x), so ff is an even function, symmetric about the yy-axis.

Answer

f(x)=x2+3f(x) = x^2 + 3; even function symmetric about yy-axis
Translating a verbal description of operations into an algebraic formula is a core skill. The table reveals the even symmetry: opposite inputs produce identical outputs because squaring eliminates the sign.

About Input-Output View

The input-output view of a function treats it as a black box: put in a value (input), get out a uniquely determined value (output), without worrying about the internal mechanism.

Learn more about Input-Output View →

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