SOLUTION: Hello I have a function f(x) represented graphically, but the function f(x) is unknown. All i know is several values of f(x) at the corresponding x. How can i identify the express

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Question 244895: Hello
I have a function f(x) represented graphically, but the function f(x) is unknown. All i know is several values of f(x) at the corresponding x. How can i identify the expression of the function?
Found 2 solutions by jsmallt9, Theo:
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
It would help if you could share these coordinates with us.

Is the graph a recognizable shape? A line? A parabola? Other?

If it is a line, then we need to find the slope. The slope can be found using the slope formula:

Then use the slope and one of the points to find the equation of the line.

In case your graph is a line, here's an example using the points (5, 8) and (6, -3):

Now we use the slope and either point to find the equation. There are a couple of ways to do this:
Using the Slope-intercept form
Using the Point-Slope form.

Since the form of the equation of a line that is a function is the Slope-intercept form, I'll use that method so save a couple fo steps:
Slope-intercept form: y = mx + b
Use the slope and a point to find b:
8 = -11(5) + b
8 = -55 + b
63 = b
Write the equation using m and b:
y = -11x + 63
Rewrite it using functional notation:
f(x) = -11x + 63

If the graph is not the graph of a line, then finding the equation is more difficult.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
graph the points and see what they look like.

if they look like a straight line, then your equation will be of the form:

ax + by = c
or:

y = mx + b

if they look like a parabola (shaped like a u or an upside down u), then your equation will be of the form:

ax^2 + bx + c = 0

or:

(x-h)^2 + k = 0

the equation depends on the shape of the graph.

that's a starting point.

from there you work back.

with a quadratic equation, you find the 0 points and solve backwards.

example:

when y = 0, x = 3 and x = -2

you have x = 3 and x = -2 which leads to the equation (x-3) * (x+3) = 0

you multiply those factors together and you have the quadratic equation.

this is exactly the reverse of how your would solve the quadratic equation to get the roots in the first place.

if you're still having trouble, send me the points and i'll take a look at it.