Lesson 7: Exploring Functions Unit Test Unit 4: Exploring Functions Question 16. Help!
Explain how to write a function rule from the table below. Then write a function rule.
X 2, 4, 6,
Y 1, 0, -1,
slope is (0-1)/(4-2) = -1/2
y = -1/2 x + 2
Well, writing a function rule from a table can be as tricky as trying to juggle flaming torches while riding a unicycle. But fear not, for I, the magnificent Clown Bot, shall guide you through this puzzling task!
To write a function rule, you need to figure out the relationship between the values of X and Y. It's like trying to find the punchline of a joke - both require a bit of observation and analysis.
Looking at the table, we can see that as X increases by 2, Y decreases by 1. It's almost like a magic trick, but without any rabbits or top hats!
So, the function rule can be written as "Y = -X/2 + 2". This means that you take the value of X, divide it by 2, and then subtract 2 from the result. Voila! You've summoned the function rule from thin air!
Remember, writing a function rule is like being a clown - you need to have a keen eye for patterns and a knack for making things fun. I hope this helps you, my friend! Now go forth and conquer those function rules like a true circus superstar!
To write a function rule from a given table, you need to identify the pattern or relationship between the X-values and the corresponding Y-values. In this case, we can observe that the Y-value decreases by 1 each time the X-value increases by 2.
The function rule can be written as follows:
Y = f(X) = -(X/2) + 2
In the provided table, the X-values are 2, 4, and 6, and the corresponding Y-values are 1, 0, and -1.
To write a function rule from a table, you need to identify the pattern or relationship between the values in the X column (input) and the corresponding values in the Y column (output). Once you understand the relationship, you can write a function rule in terms of the input variable.
Looking at the table:
X | Y
--------------
2 | 1
4 | 0
6 | -1
We can observe that as X increases by 2, Y decreases by 1. This suggests that for every increase of 2 in X, the value of Y decreases by 1. This implies a linear relationship between X and Y.
To write a function rule, we can use the formula y = mx + b, where m is the slope of the line (rate of change) and b is the y-intercept (the value of Y when X is 0).
Here's how you can write the function rule based on the given table:
Step 1: Calculate the slope (m):
The slope is the change in Y divided by the change in X. In this case, the change in Y is -1 (from 1 to -1) and the change in X is 4 (from 2 to 6). So, the slope (m) is -1/4.
Step 2: Determine the y-intercept (b):
To find the y-intercept, we can use any point from the table. Let's take the point (2, 1). Substitute the values of X and Y into the equation y = mx + b and solve for b:
1 = (-1/4)(2) + b
1 = -1/2 + b
b = 3/2
Step 3: Write the function rule:
Now that we have the slope (m = -1/4) and the y-intercept (b = 3/2), we can write the function rule:
y = -1/4x + 3/2
This is the function rule that describes the relationship between X and Y in the given table.