SOLUTION: Hi, my son and I need some serious help with this particular question: Determine whether the relation in the table below is a function, and if so, write a function rule. Table rea

Algebra ->  Functions -> SOLUTION: Hi, my son and I need some serious help with this particular question: Determine whether the relation in the table below is a function, and if so, write a function rule. Table rea      Log On


   

Question 482412: Hi, my son and I need some serious help with this particular question: Determine whether the relation in the table below is a function, and if so, write a function rule.
Table reads:
x y
-1 1
0 2
2 4
3 5
a)yes;f(x)=-1(x)
b)yes;f(x)=x/2
c)yes;f(x)=x+2
d)not a function
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One way to solve this is graphically.
Plot the given points (x, y) on a sheet of graph paper on which you drawn the x-axis (horizontal) and the y-axis (vertical).
You should see a graph like this:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%2B2%29
To get the corresponding equation, you need to know two things about the line on the graph: its slope (m) and the y-intersection (b).
The y-intersection is where the line crosses the y-axis and this is at (0, 2) and the slope (m) can be determined by picking any two points on the line and using the following formula:
m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
You can use any two points from the given list, say (-1,1) and (3, 5) as the x's and y's in the formula.
m+=+%285-1%29%2F%283-%28-1%29%29
m+=+4%2F4
m+=+1 The slope is 1.
Now use the "slope-intercept form of a linear equation:
y+=+mx%2Bb and substitute m+=+1 and b+=+2 and you get:
y+=+x%2B2 or f%28x%29+=+x%2B2 So yes, it is a function.