graphing functions question.?

Question

Hey everyone I just have a question about graphing functions in the y=f(x) form. I am given a graph of the function y=f(x) and then asked to graph different forms of it such as y=f(x)-2. But I don't know how to do that. I don't think plugging a random x value into the formula works. Please explain how to do this I am so lost. Can you also explain what the difference is when things are done inside the parenthesis such as y=f(x+3) rather than y=f(x)+3. Thanks

Answer 1

y=f(x+3) shifts it horizontally, three to the LEFT. (Since you're changing your x value, it shifts it along the x-axis.)



y=f(x)+3 shifts it vertically, three UP. (Since your x value stays the same, but you're changing your final answer, it shifts along the y-axis.)



So if you have y=f(x) and need to graph y=f(x)-2, just draw the exact same graph, but make every point 2 lower on your graph, since you're subtracting 2. If you had to add 2, you'd move it up that many.



Be careful when it's inside the parentheses though. f(x-2) would move it to the RIGHT 2. It moves A spaces along the x-axis using the equation y=f(x-A)

Answer 2

You should really stop and think about what is meant by these statements rather than hope for a quick fix. When we write y=f(x) we're describing points on a graph (x, f(x)) for what ever choice of x is given, or all that would make sense if none are specified.



for example, f(x) = 3x+1 is the set of points which contains things like (1,4) and (2, 7). It's a line.



Now, y= f(x) - 1 means to compute your y as usual, but then subtract one from it when you're done... meaning all the points on y=f(x) are now 1 lower on the graph.



y = f(x -1) means to change x before you go looking for y. That means that 2 will give you the y that 1 would have given you had you not subtracted 1. This shifts all the points over by 1 to the right.



You need to spend a lot of time graphing functions so that all these ideas become second nature, but you can't learn these ideas as simple 'rules' unless you understand the ideas as to why the rules are there.

Answer 3

okay

so your normal equation would be y=x

slope of 1, and it intercepts at (0,0)

when you have y=f(x) it is virtually the same thing. but when you take an x value such as 3, you plug it into the equation and you would get y=3

so your points would be (3,3)

if you have y=f(x+3)

you would take your x value, such as 2 and plug it in where x is and you get

y=f(2+3)

and you would do it out to get y=5

so when you have x equal to 3, y is equal to 5

so your point would be (3,5)

the parenthesis are really just incase you have negetive and what not because if you are multiplying or dividing with negetives it changes the way you are doing the problem.

you always do what is in the parenthesis first, and the outside of them



hope this helped!