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

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Question 12

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A mapping diagram of the function $g: x ightarrow x^2$ is shown below. (a) Fill in the 4 missing entries in the diagram. x 5... show full transcript

Worked Solution & Example Answer:A mapping diagram of the function $g: x ightarrow x^2$ 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

To fill in the missing entries in the mapping diagram, we compute:

  • For x=5x = 5: g(5)=52=25g(5) = 5^2 = 25 hence the entry is 25.
  • For x=3x = 3: g(3)=32=9g(3) = 3^2 = 9 hence the entry is 9.
  • For x=−6x = -6: g(−6)=(−6)2=36g(-6) = (-6)^2 = 36 hence the entry is 36.
  • For x=0x = 0: g(0)=02=0g(0) = 0^2 = 0 hence the entry is 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)=x2g(x) = x^2 is the set of all output values. From the entries:

  • The outputs are: 25, 9, 36, 0, and 49.

Thus, the range is: Range = { 0, 9, 25, 36, 49 }.

Step 3

Write 3^7 × 37 in the form 3^n, where n ∈ N.

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Answer

To express 37imes373^7 imes 37 in the form 3n3^n, we know that:

37imes37=37imes303^7 imes 37 = 3^7 imes 3^0 (because 3737 can be expressed as 303^0). Then we combine the exponents:

37imes30=37+0=373^7 imes 3^0 = 3^{7 + 0} = 3^7

So, the expression in the form 3n3^n becomes:

3nextwheren=73^{n} ext{ where } n = 7.

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