Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input(x) Output(y)
32 20
14 2
? -6
-2 -14
-10 ?
Complete the function table and write the function rule.
y = x - 12
32 - 20 = 12 ... 14 - 2 = 12 ... -2 - -14 = 12
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Verify the identity:
sin(A+B)/sin(A-B) = tan(A)+tan(B)/tan(A)-tan(B)
To complete the function table and write the function rule, we need to find the pattern or relationship between the input (x) and the output (y).
Let's start by analyzing the relationship between x and y in the given inputs and outputs:
For the first pair:
Input(x) = 32
Output(y) = 20
We notice that when the input (x) decreases by 18, the output (y) decreases by 18 as well.
For the second pair:
Input(x) = 14
Output(y) = 2
Again, we see that when the input (x) decreases by 18, the output (y) decreases by 18.
So, based on these patterns, we can conclude that for every decrease of 18 in the input (x), the output (y) decreases by 18 as well.
Now, let's apply this pattern to find the missing values:
For the third pair:
Input(x) = ? (unknown)
Output(y) = -6
Since the pattern tells us that for every decrease of 18 in the input (x), the output (y) decreases by 18 as well, we can find the missing value:
The difference between the known input (32) and the missing input is 18. So, the missing input is 32 - 18 = 14.
Therefore, the missing value is 14, which corresponds to an output (y) of -6.
For the fourth pair:
Input(x) = -2
Output(y) = -14
Using the same pattern, we find that the missing input is -2 - 18 = -20, which corresponds to an output (y) of -14.
For the fifth pair:
Input(x) = -10
Output(y) = ? (unknown)
Again, applying the same pattern, we can find the missing output by subtracting 18 from the previous output:
-14 - 18 = -32
Therefore, the missing output (y) for the fifth pair is -32, which corresponds to an input (x) of -10.
Now, let's write the function rule based on the pattern we observed:
The function rule can be written as:
y = -18x
So, the function rule is y = -18x.
To summarize the completed function table:
Input(x) Output(y)
32 20
14 2
14 -6
-2 -14
-10 -32
And the function rule is y = -18x.