Combining Functions Graphically

Hoodp

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Oct 15, 2012
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For some reason I've had some difficulty understanding combining functions graphically. If someone could help me I would greatly appreciate it.
photo.jpgIf anyone has a problem seeing this graph let me know and I'll try something else.
The questions are :
a. compute f(0)-g(0)=
b.For what values of x does g(x)=f(1)
c.For the interval [0,3] is the quantity g(x)-f(x) positive or negative? Briefly explain.
d. Compute f(x)-f(2) / x-2

Thank you in advance, I'm not necessarily looking for the answers anything would help.
 
For some reason I've had some difficulty understanding combining functions graphically. If someone could help me I would greatly appreciate it.
View attachment 2311If anyone has a problem seeing this graph let me know and I'll try something else.
The questions are :
a. compute f(0)-g(0)=
b.For what values of x does g(x)=f(1)
c.For the interval [0,3] is the quantity g(x)-f(x) positive or negative? Briefly explain.
d. Compute f(x)-f(2) / x-2

Thank you in advance, I'm not necessarily looking for the answers anything would help.
You are asking a conceptual question, and those can be difficult to answer.

There are an infinite number of ways to combine two functions into a third. Consequently, there is almost nothing meaningful that can be said generally about the graph of such a combination. I may have missed it, but are you given definitions of what f(x) and g(x) mean for this problem.

Part a asks about the combination of a(x) = f(x) - g(x) when x = 0. In other words, the rule for finding a(x) is to find the value of f(x) according to its rule, to find the value of g(x) according to its rule, and subtract the latter from the former. For example, a(x) = 2x^2 - 3x can be viewed as
a(x) = f(x) - g(x) where f(x) = 2x^2 and g(x) = 3x. Nothing mysterious about 2x^2 - 3x. But in this particular problem, your graph indicates that neither f(x) nor g(x) is defined at x = 0. If any of the functions that are being combined is not defined for some value of x, then the combination is not defined at that value. Make sense?

Question b does not technically ask about a combination of f(x) and g(x), but given a(x) = f(x) - g(x), it should be clear that the
roots (the zeroes) of a(x) are identical to the values of x where f(x) = g(x).

Question c involves a different combination. c(x) = g(x) - f(x). It should be obvious that the graph of a(x) = f(x) - g(x) and the graph of
c(x) = g(x) - f(x) are going to be mirror images of each other reflected around the x-axis. After all, a(x) = - c(x) for every x.
 
Hi Hoodp, do you understand the meaning of the symbol f(0) ? (It's called function notation.)

It looks to me like somebody drew circles around the y-intercepts of the graph. Did you add those circles; there seem to be solid dots at the intercepts. An open circle drawn on a graph denotes that the point is not included (a "hole" in the graph).

The symbol f(0) represents a number; you can see it on the graph.

The symbol g(0) represents another number; you can see that number on the graph, too.

The expression f(0) - g(0) means subtract the second number from the first.

Questions about this? :cool:
 
^^^^ thanks for the help

^^^^^^^^^^^
thanks for the help in the last post.
I added those circles when doing f(0)-g(0) so I do understand that much, my main problem is with b and c.
If you or anyone else could help me with those that would be great.

JeffM thanks for trying but it looks like your a little ahead of me. We just got into functions in my college algebra class if that helps any.
 
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What is your question about part (b)?

They want you to find the locations where function g equals the number f(1).

If you do not explain where you're stuck, I can't really know what you need. What have you done so far?

Same goes for part (c). What is it specifically that you do not understand? When subtracting one number from another, what determines whether the result is positive or negative?
 
For some reason I've had some difficulty understanding combining functions graphically. If someone could help me I would greatly appreciate it.
View attachment 2311If anyone has a problem seeing this graph let me know and I'll try something else.
The questions are :
a. compute f(0)-g(0)=
Look at the graph and determine what f(0) is. Look at the graph and determine what g(0) is. Subtract!

b.For what values of x does g(x)=f(1)[/quote]
Look at the graph and determine what f(1) is. Since y= f(x) is a specific height above the x-axis, draw, or imagine, a horizontal line at that height. Where does the graph of y= g(x) cross that line?

c.For the interval [0,3] is the quantity g(x)-f(x) positive or negative? Briefly explain.
a- b is positive only if a> b, negative only if a< b. Where on the graph is g(x) larger than f(x)? Where is it smaller? Do you understand that if g(x) is larger than f(x) then it will be above on the graph and vice-versa for "less than"?
 
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