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kumar_23
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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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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).
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.
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.
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?
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.
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'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!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?
As far as I know, when it's only a variable (be it x, a, b etc.), we take it as 1.
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.
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.
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.
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).
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.