Question

A series of tile patters is shown below. Consider the function that represents the number of white tiles in each figure.

Select all the statements that are true


-W(n)=4n+4 represents the function.

-W(n)=4n+8 represents the function.

-Input values for the function are natural numbers.

-Input values for the function are the number of white tiles in each figure.

-The function is continuous.

-Figure 6 will have 10 white tiles.

-Figure 8 will have 36 white tiles.

Answer 1

• W(n)=4n+4 represents the function.

• Input values for the function are natural numbers.

• Figure 8 will have 36 white tiles

Explanation:

–W(n)=4n+4 represents the function.

TRUE - For figure 1, this function gives W(1) = 4·1+4 = 8, the number of white tiles. It also gives correct values for the other figures shown.

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–W(n)=4n+8 represents the function.

FALSE - See the other W(n) function above. This function does not give correct values for the figures shown.

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–Input values for the function are natural numbers.

TRUE - the figures are numbered using natural numbers, so natural numbers are the input to the function

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–Input values for the function are the number of white tiles in each figure.

FALSE - The description of the function is that the number of white tiles is its output, not its input.

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–The function is continuous.

FALSE - the domain of the function is natural numbers. It is undefined for numbers other than that, so is not continuous.

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–Figure 6 will have 10 white tiles.

FALSE - using the definition of W(n) above, we find W(6) = 28, not 10.

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–Figure 8 will have 36 white tiles.

TRUE - W(8) = 36