Complete Function Machines and Tables
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Give the correct answers in each space. (Top section shows three functional boxes with inputs: For the first box ($x+4$), inputs are $x, 2, -1, 0, 15$. For the second box ($4x$), inputs are $x, 2, -1, 0, 1$. For the third box ($5m-6$), inputs are $m, 4, -2, 12, 20$. Below this is the section 'Complete the tables below.') a) For $y=2x$, input values $1, 2, 3, 15$. b) For $n=6n+3$, input values $-1, 0, 2, 10$. c) For $y=-3x+2$, input values $5, 4, 3, -8$.
This question includes visual content: The image displays two sections. The top section contains three 'function machine' boxes taking inputs (e.g., $x$, $m$) and outputting results based on expressions: $x+4$, $4x$, and $5m-6$. Each has a list of specific input values to evaluate. The bottom section contains three tables (labeled a, b, c) corresponding to expressions $y=2x+...$, $n=6n+3$, and $y=-3x+2$, where the user must complete the output values for given inputs.
Animated Video Solution
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Step by Step Written Solution
In this problem, we are asked to complete the tables by applying a given formula or rule to several input values. We will go through each part one by one.
Completing Input-Output Tables
Let's focus on part a first. The rule is given by the equation y equals two x plus nine.
Part A
| x | 1 | 2 | 3 | 15 |
|---|---|---|---|---|
| y | ? | ? | ? | ? |
First, we substitute x equals one into the formula. Two times one plus nine gives us eleven.
Next, for x equals two, two times two is four, and adding nine gives us thirteen.
When x is three, two times three is six. Adding nine results in fifteen.
Finally, for x equals fifteen, two times fifteen is thirty. Adding nine gives us thirty-nine.
Now let's look at part b. The rule here is n equals six m plus three.
Part B
| m | -1 | 0 | 2 | 10 |
|---|---|---|---|---|
| n | ? | ? | ? | ? |
If m is negative one, six times negative one is negative six. Adding three gives us negative three.
For m equals zero, any number times zero is zero, so we are just left with three.
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