Create a function rule for the following:
x 0 3 6
f(x) -5 -3 -1
How do I create a function rule? I forgot how to and nowhere online is giving me a good example of how to.
note that as x goes up by 3, y goes up by 2
That means the slope is 2/3
So, first guess is y = 2/3 x
But, when x=0, y==5, so now we have
y = 2/3 x - 5
or,
2x-3y = 15
Look at the x values. ...
Next look at the y values. ...
The y values in this table are going up five every time. ...
Go back to the first x. ...
You need to add 3. ...
Once you decide on a rule, make sure it works for the other x values.
The function is y = 5x + 3.
Replace the y with the f
and if this doesn't help try watching this video my dear.
Write a Function Rule: An Application (Algebra I)
just search that um an skip until about 0:30
Your funtion of f(x) = 5x + 3 does not work for a single one of the 3 points.
You have 3 points given:
(0,-5), (3,-3) and (6,-1)
First you have to decide if the function is linear, that is, do the
points lie in a straight line. Let's use slope
slope between first two = (-3+5)/(3-0) = 2/3
slope between last two = (-1+3)/(6-3) = 2/3
Yes, do do form a straight line, and the equation is
f(x) = (2/3)x + b
but we can also see that (0,-5) is the y-intercept
so f(x) = (2/3)x - 5
To create a function rule, you need to find a relationship between the values of x and the corresponding values of f(x). In this case, we have three data points: (0, -5), (3, -3), and (6, -1).
One method to find the function rule is to determine the pattern or rule that relates the x-values to the corresponding f(x)-values. In this case, notice that as x increases by 3 units, the corresponding f(x) increases by 2 units. Thus, the function rule involves multiplication and addition.
Let's start by finding the multiplication factor:
- The x-values increase by 3 units (0 to 3, 3 to 6).
- The corresponding f(x)-values increase by 2 units (-5 to -3, -3 to -1).
To find the multiplication factor, we can divide the change in f(x) by the change in x.
Change in f(x) = 2 units
Change in x = 3 units
Multiplication factor = (Change in f(x)) / (Change in x)
= 2 / 3
Now let's find the starting point or constant term:
- When x = 0, f(x) = -5.
To find the constant term, we can subtract the multiplication factor times the x-value from the f(x)-value.
Constant term = f(x) - (Multiplication factor * x)
= -5 - (2 / 3) * 0
= -5
Putting it all together, the function rule for the given data points is:
f(x) = (2 / 3) * x - 5.
This means that for any value of x, you substitute it into the function rule, and the result will be the corresponding f(x) value.
For example:
- f(9) = (2 / 3) * 9 - 5
= 6 - 5
= 1
Therefore, using the function rule f(x) = (2 / 3) * x - 5, we can find the corresponding f(x) value for any given x.