Transformations of Functions- graphing y=f(x)-4?

In summary, to graph y=f(x)-4, you need to know the original graph of f(x) and then shift it down four units. However, f(x) must be specified before the graph can be drawn. When using a graphing calculator, you can graph y=f(x)-4 by inputting the equation and shifting it down four units, but the function f(x) must be defined beforehand. It is not correct to assume f(x)=0 or any other value without being specified.
  • #1
kumar_23
38
0
How would you graph y=f(x)-4? I am not sure how the original graph looks like y=f(x) either. Also, if i were to graph this using a graphing calculator, how would that be done?
 
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  • #2
Erm.. you need to know what f(x) is. f(x) can be any function of x, so it is impossible to sketch it until you say what it is!
 
  • #3
I think the answer kumar wants is:

You take the graph of f(x) and shift it down four units. (Assuming f:R->R).
 
  • #4
I think ZioX is right. From what I remember, f(x) is the same thing as y so it's saying (IMO): y = -4. So it would be shifted down 4 units and you should have a horizontal line.
 
  • #5
ZioX said:
I think the answer kumar wants is:

You take the graph of f(x) and shift it down four units. (Assuming f:R->R).

Well yes, but in the original post he says he doesn't know what the graph of the function f(x) looks like. Thus, he will need to plot that first then shift it four units down.
 
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  • #6
Prim3 said:
I think ZioX is right. From what I remember, f(x) is the same thing as y so it's saying (IMO): y = -4. So it would be shifted down 4 units and you should have a horizontal line.

Huh? That's not what ziox is saying. How do you get that the graph is even a straight line? We do not know the form of f(x). It could be f(x)=x^2, in which case y=x^2-4; clearly not the straight line y=-4!
 
  • #7
In a graphing calculator, you should graph this cristo: y = f(x) - 4 and you will get a straight line 4 units down. It's going to be a horizontal line and the coordinates would be: (0,-4). I tried it and that's what I got. Maybe I did it wrong but I'm not completely sure about it.
 
  • #8
Prim3 said:
In a graphing calculator, you should graph this cristo: y = f(x) - 4 and you will get a straight line 4 units down. It's going to be a horizontal line and the coordinates would be: (0,-4). I tried it and that's what I got. Maybe I did it wrong but I'm not completely sure about it.

Your calculator is assuming f(x)=0, since you have not defined it, thus it sees the equation as y=-4 and plots this.

Again, the function f(x) must be specified before it can be sketched.
 
  • #9
Exactly. But, since he didn't specify what f(x) is, I took it as 0 as well and ended up with y = -4. Wouldn't that work then?
 
  • #10
Prim3 said:
Exactly. But, since he didn't specify what f(x) is, I took it as 0 as well and ended up with y = -4. Wouldn't that work then?

If f(x)=0, then y=f(x)-4 will become y=-4, but why are you taking f(x)=0? Why not take f(x)=17x, or f(x)=x^9? The function f(x) must be specified before the graph can be drawn.
 
  • #11
I'm taking it as a 0 because he didn't specify any other number. If he had specified 1, 2, 3, 4 etc. then I have would've used that. When I was doing this in my homework, an exact question I came upon was y = f(x) - 6 and we had to assume that f(x) = 0 since f(x) wasn't defined.

It's like taking this equation: x^2 + 4x - 5. It's the same as: (1)^2 + 4(1) - 5 because x isn't defined so we take it for 1. Right? At least that's how I learned it.
 
  • #12
Prim3 said:
I'm taking it as a 0 because he didn't specify any other number. If he had specified 1, 2, 3, 4 etc. then I have would've used that. When I was doing this in my homework, an exact question I came upon was y = f(x) - 6 and we had to assume that f(x) = 0 since f(x) wasn't defined.

f(x) isn't a number, it's a function. If you evaluate it at a certain value of x, then it will have a numerical value, but before you do that, it is a function!

Like I said earlier; there is no reason to assume f(x)=0, just because the OP has not told us what it is!

It's like taking this equation: x^2 + 4x - 5. It's the same as: (1)^2 + 4(1) - 5 because x isn't defined so we take it for 1. Right? At least that's how I learned it.

I don't really know what you're doing here. It seems that you are evaluating the function at the point x=1.

We definitely need to know the value of the function before we can sketch the graph (wow, how many times have I said that in this thread? :rolleyes: )
 
  • #13
Yes, I know it's a function. Maybe the way we learned things is different.

Also, for the 2nd part, if you had to say what x was without it being defined at all, what would you say? As far as I know, when it's only a variable (be it x, a, b etc.), we take it as 1.
 
  • #14
Prim3 said:
Also, for the 2nd part, if you had to say what x was without it being defined at all, what would you say?
I'd say it was x. If you're not told the value of x at which to evaluate the function, then you cannot just pick anything!
As far as I know, when it's only a variable (be it x, a, b etc.), we take it as 1.

I'm sure that you're confusing things here. You probably took x=1 when you were required to evalute the function at x=1; i.e. you wanted f(1)
 
  • #15
I was speaking in general and not keeping f(x) in mind regarding the variables being 1. What I'm trying to say is consider this equation: x + 5. If we were to re-write that in another way, it can be 1x + 5. x isn't defined with 1, what I meant to say is explained in that equation. Maybe I said it wrong. Off to bed now; school tomorrow.
 
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  • #16
thanks for your help!
 

FAQ: Transformations of Functions- graphing y=f(x)-4?

What is the general process for graphing y=f(x)-4?

The general process for graphing y=f(x)-4, or any function, involves finding key points on the graph, plotting them, and then connecting them to create the full graph. In this specific case, you would first need to find the y-intercept, which is -4 in this case. Then, you can choose a few x-values and use the given function to find the corresponding y-values. Plot these points and connect them to create the graph.

How does the value of -4 affect the graph of y=f(x)-4?

The value of -4 in the function y=f(x)-4 represents the vertical shift of the graph. This means that the entire graph will be shifted down 4 units on the y-axis. This can be seen by comparing the original function y=f(x) to the new function y=f(x)-4. The graph will still have the same shape, but it will be lower on the y-axis by 4 units.

Can you provide an example of a real-world scenario where y=f(x)-4 would be used?

One example of a real-world scenario where y=f(x)-4 would be used is in the field of economics. In economics, the function y=f(x) often represents a demand curve, which shows the relationship between the price of a product and the quantity demanded. By subtracting 4 from the function, you are essentially shifting the entire demand curve down, which could represent a decrease in demand due to factors such as a decrease in consumer income.

How do you determine the domain and range of y=f(x)-4?

The domain of any function is the set of all possible x-values, while the range is the set of all possible y-values. In the case of y=f(x)-4, there are no restrictions on the x-values, so the domain remains the same as the original function, which is all real numbers. However, the range will be shifted down by 4 units, so the new range will be all real numbers - 4, or (-∞, -4).

Is there a specific method for graphing y=f(x)-4 on a coordinate plane?

There are many different methods for graphing functions on a coordinate plane, but one common method is to create a table of values. In this case, you would choose a few x-values, plug them into the function y=f(x)-4 to find the corresponding y-values, and then plot those points on the coordinate plane. You can also use the vertical shift method, where you start with the original function y=f(x) and then shift the entire graph down 4 units on the y-axis to create the new graph y=f(x)-4.

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