Graphing of functions: f(x) = |x|^x
Not what you're looking for?
Use Graphing Utilities to examine a function of x : f(x) = |x|^x Lots of analysis of grpah of f(x)=|x|^x so please inspect the attachment for full treatise
Purchase this Solution
Solution Summary
A graphing utility is used to graph the function f(x) in the range -3<=x<=3, -2<=f(x)<=2
f(x) = |x|^x for x not = 0
f(x) = 1 for x = 0
The domain of f(x) is then determined
Zoom and trace functions of the utility are then used to determine the limit of f(x) as x tends to zero
The reasons why f(x) is continuous for all real numbers is then explained.
From the graph the slope at (0,1) is then visually estimated
Solution Preview
Lots of graphs and explanations so look at the attachment as I cannot paste the graphs here.
(a) We graph f(x) using the graphing utility [1] for the range -3 ≤ x ≤ 3, -2 ≤ y ≤ 2
The settings to do this are shown in window below
The resultant graphed function is then reproduced below
Graphing of the function f(x) = |x|x in the range -3 ≤ x ≤ 3, -2 ≤ y ≤ 2
Domain of f(x) is the range for all real valid x and can be seen to be from
-infinity to + infinity
(b) We use the zoom facility by examining the graph and zooming in on the area of the graph around (0,1). I have achieved this by simply altering the x range so that x extends from -0.2 to +0.2 and y extends from 0.0 to +2.0 using the graphing tools limit values. The zoomed graph can be seen below
We can see that the limit of f(x) = |x|x as x tends to 0 is 1
(c) The function f(x) = |x|x is continuous for all real numbers because there exists a real value of f(x) for all values of x; even at x=0 f(x) is defined. Graphically speaking this means that the curve of f(x) is unbroken at every point for real x
(d) ...
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts