Looks like a typo in the book.Astraithious said:Homework Statement
Write F(x)= x2-5|x| as a piecewise function
Homework Equations
The Attempt at a Solution
I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)
but my book says that it comes out to be
x2-5
x2-5(-x)
I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!
Astraithious said:Homework Statement
Write F(x)= x2-5|x| as a piecewise function
Homework Equations
The Attempt at a Solution
I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)
but my book says that it comes out to be
x2-5
x2-5(-x)
I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!
Your answers appear to be identical with the book's so I don't know what your problem is. It would then be usual to write it in the form that Samy did, and also when setting out piecewise functions you have to indicate the range either side of the form.Astraithious said:Homework Statement
Write F(x)= x2-5|x| as a piecewise function
Homework Equations
The Attempt at a Solution
I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)
but my book says that it comes out to be
x2-5
x2-5(-x)
I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!
No, the book has x2-5 instead of x2-5x.epenguin said:Your answers appear to be identical with the book's so I don't know what your problem is.
An absolute function is a mathematical function that returns the positive value of a number, regardless of its original sign. It is represented by the symbol |x|.
A piecewise function is a function that is defined by multiple sub-functions, with each sub-function being defined for a specific interval or set of intervals. This allows for different rules to be applied to different parts of the function's domain.
An absolute function is a specific type of function that always returns the positive value of a number, while a piecewise function is a more general concept that can combine multiple functions to create a more complex overall function.
To graph an absolute function into a piecewise function, you first need to identify the intervals in which the function will change. Then, for each interval, you will graph the corresponding sub-function. Finally, you will connect the different parts of the graph to create a piecewise function.
Absolute functions into piecewise functions are commonly used in economics, physics, and engineering to model complex relationships and systems. For example, they can be used to model the demand for a product based on different price ranges, the acceleration of an object based on different forces, or the flow of traffic through a city at different times of the day.