Which function rule represents the data in the table?
x|-3|-2|-1|0|1
y|-1|2|5|8|11
The answer choices are
1. y=-3x-8
2. y= 1/3x-8
3. y= 1/3x+8
4. y= 3x+8
Please state the answer and how you got it. I want to be able to do this on my own in the future. Thanks. Also, I chose D(4).
note that as x changes by 1, y changes by 3
So, start with y=3x
But, y(0) = 8, so use y=3x+8
check to be sure it fits all the pairs. It does.
To determine the function rule that represents the data in the table, we need to observe the relationship between the x-values and the corresponding y-values.
Let's begin by examining the changes in the y-values as the x-values increase by one unit each time.
From x = -3 to x = -2:
- The y-value increases from -1 to 2. The change in y is 2 - (-1) = 3.
From x = -2 to x = -1:
- The y-value increases from 2 to 5. The change in y is 5 - 2 = 3.
From x = -1 to x = 0:
- The y-value increases from 5 to 8. The change in y is 8 - 5 = 3.
From x = 0 to x = 1:
- The y-value increases from 8 to 11. The change in y is 11 - 8 = 3.
We can see that the pattern in the changes of the y-values is consistent: each time the x-value increases by 1, the y-value increases by 3.
Now, let's look at the y-intercept (the value of y when x = 0) from the table. When x = 0, y = 8.
Putting all this together, the function rule that represents the data in the table is:
y = 3x + 8
Therefore, the correct option is 4. y = 3x + 8.
A note on choosing option D(4) - Since the data in the table includes only x-values up to 1, we cannot directly determine the accuracy of option D(4) without extending the table or calculating based on the pattern observed in the data. Given that option 4 (y=3x+8) satisfies the pattern observed in the data, it is the most reasonable choice.
To determine which function rule represents the data in the table, we need to observe the relationship between the x-values and y-values.
First, let's look at the pattern in the table: as x increases by 1, y increases by 3.
Now let's consider the slope-intercept form of a linear equation, which is y = mx + b.
In this form, "m" represents the slope, and "b" represents the y-intercept.
Looking at the pattern in the table, we can see that the slope is 3 because for every increase of x by 1, y increases by 3.
Next, we need to determine the y-intercept. From the table, we can see that when x = 0, y = 8. Therefore, the y-intercept is 8.
Putting it all together, we have the function rule:
y = 3x + 8
Based on the given answer choices, the correct function rule that represents the data in the table is option 4: y = 3x + 8.
Regarding your choice of D(4), it seems like you might be referring to evaluating the function rule for x = 4. If that's the case, you can substitute x = 4 into the function rule we found (y = 3x + 8) to find the corresponding y-value. In this case, y = 3(4) + 8 = 12 + 8 = 20. Therefore, when x = 4, y = 20.
I hope this explanation helps you understand how to determine the function rule from a data table.