Find the rule for the mapping: 0->5, 1->6, 2->9, 3->14, 4->21, 5->30.

March 18, 2026Mathematics

ScanSolve AI Answer

March 18, 2026

Answer

$f(x) = x^{2} + 5$

Step 1: List the given mappings.

\begin{align*} &0 \mapsto 5,\\ &1 \mapsto 6,\\ &2 \mapsto 9,\\ &3 \mapsto 14,\\ &4 \mapsto 21,\\ &5 \mapsto 30. \end{align*}

Step 2: Subtract 5 from each output value.

\begin{align*} &5 - 5 &= 0,\\ &6 - 5 &= 1,\\ &9 - 5 &= 4,\\ &14 - 5 &= 9,\\ &21 - 5 &= 16,\\ &30 - 5 &= 25. \end{align*}

Step 3: Compare to input squared.

\begin{align*} &0^2 &= 0,\\ &1^2 &= 1,\\ &2^2 &= 4,\\ &3^2 &= 9,\\ &4^2 &= 16,\\ &5^2 &= 25. \end{align*}

Step 4: The pattern matches, so the rule is output = input squared + 5.

The rule is $f(x) = x^2 + 5$ .

f(x) = x^{2 + 5}

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