A mapping diagram of the function $g: x \mapsto x^2$ is shown below. (a) Fill in the 4 missing entries in the diagram. \[ \begin{array}{|c|c|} \hline x & g(x) = x^2 \\ \hline 5 & 25 \\ 3 & 9 \\ -6 & 36 \\ 0 & 0 \\ \hline \end{array} \] (b) Write down the range of the function $g(x)$, as shown in the diagram. Range = { 0, 9, 25, 36, 49 } (c) $g(3^7) = 3^7 \times 3^7$. Write $3^7 \times 3^7$ in the form $3^n$, where $n \in \mathbb{N}$. $3^7 \times 3^7 = 3^{14}$

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A mapping diagram of the function $g: x \mapsto x^2$ is shown below - Junior Cycle Mathematics - Question 12 - 2018

Question 12

$A-mapping-diagram-of-the-function-$g:-x-\mapsto-x^2$-is-shown-below-Junior Cycle Mathematics-Question 12-2018.png$

A mapping diagram of the function $g: x \mapsto x^2$ is shown below. (a) Fill in the 4 missing entries in the diagram. \[ \begin{array}{|c|c|} \hline x & g(x) = x^... show full transcript

Worked Solution & Example Answer:A mapping diagram of the function $g: x \mapsto x^2$ is shown below - Junior Cycle Mathematics - Question 12 - 2018

Step 1

Fill in the 4 missing entries in the diagram.

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Answer

The function $g(x) = x^2$ produces the following results:

For $x = 5$ : $g(5) = 5^2 = 25$
For $x = 3$ : $g(3) = 3^2 = 9$
For $x = -6$ : $g(-6) = (-6)^2 = 36$
For $x = 0$ : $g(0) = 0^2 = 0$

Step 2

Write down the range of the function g(x), as shown in the diagram.

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Answer

The range of the function $g(x)$ includes all possible output values:

Range = { 0, 9, 25, 36, 49 }

Step 3

g(3^7) = 3^7 \times 3^7. Write 3^7 \times 3^7 in the form 3^n, where n ∈ N.

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Answer

Using the property of exponents, we can combine the terms:

$g(3^7) = 3^7 \times 3^7 = 3^{7+7} = 3^{14}$

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