Parabolic Function: Graph of y=ax^n

  • Thread starter Thread starter batballbat
  • Start date Start date
  • Tags Tags
    Function
Click For Summary
The graph of the function y=ax^n can be derived from y=x^n by adjusting the coefficient a. A positive a results in a narrower graph as its value increases, while a smaller positive a makes the graph wider. When a is negative, the graph is reflected across the x-axis, maintaining the same shape but reversing its direction. For instance, y=-x^2 retains the shape of y=x^2 but opens downward. Understanding these transformations allows for predicting the graph's appearance based on the value of a.
batballbat
Messages
127
Reaction score
0
how can the graph of the function y=ax^n be obtained from the graph of y=x^n if a is positive?negative
 
Physics news on Phys.org
If you graph two functions, y=x^2 and y=5x^2 you will notice the first graph appears "fatter" and the second graph is "skinnier".
As you increase the coefficient a the more narrow the graph becomes.
As you decrease the coefficient a the wider the graph becomes.
I would experiment with this concept until you notice a mathematical pattern by which you can predict the graph's appearance at any a.
 
When a is negative, the graph is reflected about the x-axis. For example, the parabola y=-x^2 has the same shape as y=x^2, but is pointing down instead of up.
 

Similar threads

Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Inverse Functions: x=f(y) and X=f^-1(y)
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Questions about these Trigonometry Graphs involving sin() and cos()
  • · Replies 3 ·
Replies
3
Views
2K
MHB Limit of Trigonometric Function....2
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Finding the derivative of a characteristic function
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Optimization with integers as results
  • · Replies 3 ·
Replies
3
Views
1K
MHB How to Find the Limit of (1 - x)/[(3 - x)^2] as x Approaches 3?
  • · Replies 5 ·
Replies
5
Views
1K
High School Why is Big-O about how rapidly the Taylor graph approaches that of f(x)?
  • · Replies 19 ·
Replies
19
Views
4K
High School Why the derivative of area is related to the graph of the function
  • · Replies 12 ·
Replies
12
Views
3K