How do you graph g(x) in terms of f(x) for absolute function?

In summary, the problem discussed is about how to plot g(x)= f(|x|) and g(x)=|f(x)|, where g is in terms of f. The function g will not necessarily be a V shape unless f(x) is a linear function. The expression g(x)=|f(x)| means that the graph will reflect around the x-axis in intervals where f(x) is negative. An example is given with f(x)=x^2-1 to illustrate this concept.
  • #1
Analysisfreak
2
0
The graph of g is interm of f. So how to plot g(x)= f(|x|) and of g(x)=|f(x)|. Is it jus a 'V' shape one.This problem is in Spivak Textbook, Chapter 4. Thanks to all.:confused:
 
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  • #2
Well, it won't be a V function, unless f(x) is a linear function, that is of the form f(x)=kx+b. However, the expression g(x)=|f(x)| means that your g function will be graphed in that manner that in whatever interval f(x) is positive, g(x) will remain unchanged, however, in whatever interval f(x) is negative, your g(x) will be reflected around the x-axis. Say for example that f(x)=x^2-1. then this function is negative from -1 to 1. so this portion of the graph will be reflected around x-axis while the other part will remain unchanged if g(x)=|f(x)|=|x^2-1|
 

1. What is an absolute function?

An absolute function is a type of mathematical function that is defined as f(x) = |x|, where |x| represents the absolute value of x. This function outputs the positive value of any input, regardless of whether the input is positive or negative.

2. How do you graph an absolute function?

To graph an absolute function, you can plot points by choosing various values for x and finding the corresponding y values using the function f(x) = |x|. The graph will consist of two straight lines intersecting at the origin, with the line passing through the origin having a slope of 1.

3. What is the domain and range of an absolute function?

The domain of an absolute function is all real numbers, as any value of x can be plugged into the function. The range of an absolute function is also all real numbers, but the output will always be a positive value.

4. How do you solve equations involving absolute functions?

To solve an equation involving an absolute function, you can split the equation into two separate equations, one with the positive input and one with the negative input. Then, you can solve for both cases and find the solution set by combining the two sets of solutions.

5. What are some real-life applications of absolute functions?

Absolute functions can be used to model various real-life scenarios, such as calculating distance, velocity, and acceleration in physics problems. They can also be used in economics to analyze production and cost functions, as well as in computer science to create algorithms for data processing and optimization.

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