Question

how do i get the function f from a graph?

Answer 1

you use these equations after picking two points that lie on the same line
y-y0=m(x-x0) and m=(y-y0)/(x-x0)

Answer 2

problem is that the graph has a curve and not a straight line

Answer 3

Usually you take test points.
In higher maths, f(x) is just a fancy way of saying "y" in algebra.

so, you look at the graph and find points on it.
say your graph passes through these points:
(0,2) (1,3) (2,4) (3,5)

You can then figure out the function by finding the slope
3-2
m= ----
1-0
so, m=1
now for slope intercept form.
3=(1)(1)+b
b=2
so the function for this figurative graph would be
f(x)=x+2

Answer 4

with curve it is a little more difficult... you still look at the different points and try and glean a pattern from them.

Answer 5

The function will be y because f(x) = 2x + 4 is kinda like saying y = 2x + 4 which x = 2
f(2) = 2(2) + 4
F(x) = 8
our poinjt is (2,8)

y = 2x + 4
y = 2(2) + 4
y = 8
our point is (2,8)

Answer 6

ill try to post an attachment

Answer 7

there you go

Answer 8

f(-2) means what is the value of y when x=-2
so u go to -2 on the x axis and draw a vertical line and see when it intersects the curve

Answer 9

would that be 0?

Answer 10

yup

Answer 11

but how would i make that a function?

Answer 12

a. for this problem you just look at the Y value when X=-2 that is what f(-2) suggests! So, when x=-2 y=0. so your answer for a is:

f(-2)=0

b. The domain of a function is all possible x values for the function. since this function does not exist before -4 and does not exist after 4, the domain of this function is [-4,4] make sure you use brackets because the dots at the end of the graph are solid not open, if they were open you would use parentheses. so your answer the b. is:

[-4,4] or \[-4\le x \le 4\]

c. This is similar to a except opposite. now we are taking a y value and pointing out all x values that yield that y value. on this graph, y or f(x)=2 when x=-4, and when x=-1 so, your answer for c is:

f(-4)=2 and f(-1)=2

d. The range of f is similar to b except you are looking for all possible Y values. Since your graph does not go below the x axis (y=0) and the graph does not raise above 5, we can say the the range of f is [0,5] again here we use brackets because the line does touch both 0 and 5. so, the answer to d is:

[0,5] or \[0\le y \le 5\]

e. here you are just asked to evaluate a y value, just like in a. however they throw you a curve ball and there is no y value when x=-5! In mathematical terms, that means that f(x) simply does not exist at this point. The way we denote that f(x) does not exist is by puting the letters DNE which stand for, you guessed it, Does Not Exist. So, your answer for e is:

f(-5) DNE

Answer 13

hope that helps, let me know if you have another question!

Answer 14

wow:)

Answer 15

:)

Answer 16

O.O wow i think that helps :)