X. F(x)
4. 13
2. 7
0. 1
-1. -2
using the table, what is the value of f(-1)?
Write a linear function equation for this table of values.
Using this equation or the table itself, find the value of f(1)
I don't understand this.
X. F(x)
4. 13
2. 7
0. 1
-1. -2
using the table, what is the value of f(-1)?
Write a linear function equation for this table of values.
Using this equation or the table itself, find the value of f(1)
I don't understand this.
K so the question is saying that there is a function such that plugging in any x into the function will give you a value for y=f(x) as listed in the table.
Using this, we can think of the table as telling us this:
Now as for making a function. What can we decide from the table? It looks like if x =0, f(x)=f(0)=1. So it looks like we need to have a constant that isn't multiplied by any x.
Next, lets looks at the values, how can we turn 2 into 7 and 4 into 13?
Looks like . Does this make sense how we came to this? It can be a bit of a trial and error process.
Let's test it.
Can you find now?
Nice avatar, Kasper !
Otherwise, you might want to consider a more straightforward algebraïc way.
Your problem strongly suggests that a linear relationship exists between and . This is equivalent to saying that , for some and , .
1. Find
You have some values of the function (actually, only two are required). You can say that :
We can slightly reformulate this :
And now, we get smart ! We divide both equations together :
Which is equivalent to :
Now we simplify the fraction :
2. Find
Now that we know , this is easy : we know that : we can use a pair of values :
Since , we get :
3. Conclusion
You are done : you have found the linear relationship between and :
Let's check those results :
-->
-->
-->
-->
Now that we can find from with a simple linear formula, let's answer the last part of the question : substitute to find the value of :
Done !
_________________
Does it make sense ?
Hello, brianfisher1208!
. . .
Using the table, what is the value of ?
Um . . . -2 ?
A linear function has the form: .Write a linear function equation for this table of values.
And we must determine and
We can use any two values from our table.
For example:
. .
Subtract [2] - [1]: .
Substitute into [1]: .
Therefore: .
Using this equation or the table itself, find the value of
Interesting! As you can see, Brian, Soroban chose to solve by substitution a system of linear equations in order to find and , while I decided to arrange the equations to allow a division that will get rid of an unknown, making solving easy. Two equivalent solutions to one problem (although mine was a bit longer).
Thanks Soroban, I didn't know the command \boxed, I was sort of deceived my function didn't appear in math font