Questions: Which two functions could complete this function machine? × 7 k ×6k +6 ÷ 7 k +7k +6k

Transcript text: Which two functions could complete this function machine? $\times 7 k$ ×6k $+6$ $\div 7 k$ +7k +6k

Solution

Solution Steps

Step 1: Analyze the problem

The input is 'k'. The output is '7k'. We need to find two functions that can transform 'k' into '7k'.

Step 2: Find the first function

The first function needs to transform 'k' into a value that the second function can use to produce '7k'. Multiplying 'k' by 7 transforms 'k' into '7k'.

Step 3: Find the second function

The second function needs to work with the result of the first function to produce '7k'. If 'k' is multiplied by 7 to create '7k' by the first function, adding 0 would give '7k + 0 = 7k' by the second function. While the given option tiles do not include "+ 0", they do include "+ 6k" and "-6k". Choosing these two as the second function will result in 7k. Applying the function "x7" followed by "+6k" will turn "k" into "7k". Applying the function "x7k" followed by "+/-6k" will result in "7k +/- 6k".

Final Answer:

The two functions are ×7 and + 0. Since +0 is not in the given options, x7 and -6k can be chosen as the first function. Following this, +6k can be chosen as the second function. The two functions can be either x7 and +6k, followed by -6k, or x7k followed by -6k, then +6k.

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