Would someone please help me with this? They want me to graph the function and compare the graph with f(x)=x
If you answer please write out the steps that you take to get there and keep it simple!
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well, do you know what the graph f(x) = x looks like?
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g(x) = x + 5 means that g(x) is just f(x) shifted up by 5 units
How did you come to that conclusion? What steps did you take?
The graph itself makes sense but I have more problems like this to do and I still don't understand it.
@bookish610 I can try to explain if you still don't understand?
I am still not understanding this. Please do explain it!
@bookish610 Sorry, OpenStudy crashed on me. I will explain
In the function f(x)=x, we can note how this specific function goes right through the origin, as Vocaloid drew up for you. This simply states it has no x-intercept or y-intercept, obviously. (We don't have any numbers within the equation to actually have anything :) )
Now we look at g(x)=x+5. The '+5' portion of this equation is our vertical shifts, with Vocaloid did a good job drawing up. Pre-calculus does a good job explaining bout the vertical and horizontal shifts of equations and graphs. I will show you a technique my teacher taught me to remember this stuff.
The best thing to remember with the horizontal shifts is they get all topsy-turny, opposite in their manner, soooo, that +1 actually is a shift in the negative direction. If it was (x-1)^2 it would be a shift to the positive direction. However don't worry about that if you're not into that yet.
The point of my drawing is to interpret the "+2" because that resembles the "+5" in your g(x) function. It is the visitor of 'x', so it will be a vertical shift. The next step is to determine if it is a upward (positive) shift or downward (negative) shift. It was a positive shift up 5 units on the y-axis.
If you wanted to compare the graph of g(x)=x-6 to f(x)=x it would look like this
Graphing functions is easy when you learn the basics. If you ever need help, let me know.