Power Functions and Variation on a Graphing Calculator
Key Questions
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First, let's remember what a power function is. For any constant real number
p and real variablex , functions of the formf(x)=x^p are called power functions ofx .What does it mean that a power function
x^p models a given set of ordered pairs? We know that, in general, the graph of a functionf is the set of ordered pairs(x, y) , such thaty=f(x) .So, a given set of ordered pairs modeled by a power function corresponds to a set of points contained in the graph of the power function.
The problem becomes that of finding the equation of the power function given that we know the coordinates of a number of points of its graph. This is solved by solving the resulting system of equations.
Example:
Consider a given set of ordered pairs:
{(1, 2), (2, 5), (3, 10)} . This corresponds to the pointsA(1, 2) ,B(2, 5) andC(3, 10) contained in the graph of the power functionf(x)=x^p .So, we have the following equations:
(1) 1^p=1
(2) 2^p =4
(3) 3^p=9 We see that
p=2 , therefore the power function isf(x)=x^2 This is a simple illustration of the general idea. In practice, the problems can be more complex.
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All you need to do is go to your
y= button, and type the function in as you would for any other function. You may need to use the "carrot" key (located below the "Clear" button on the upper right side of the calculator) a fair few times. Watch your parenthesis.For example, if I wanted to graph
y = 3(5^x) , then I would enter the following:3, (, 5, ^, x, ).
In words:
Three, left bracket, carrot, x, right bracket.
As I mentioned, just watch your parenthesis, as they are probably what most people are likely to mess up. If you pay attention to this you should be good :)