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Precalculus: 4.1
Precalculus: 4.1
21
Mathematics
10/26/2015

Term
 a^x+a^y
Definition
 a^(x+y)
Term
 a^x/a^y
Definition
 a^(x-y)
Term
 (ab)^x
Definition
 a^(x)b^(x)
Term
 (a^x)^(y)
Definition
 a^(xy)
Term
 a^(0)
Definition
 1
Term
 a^(-x)
Definition
 (1/a)^(x)
Term
 Graphing an Exponential Function Where a>1
Definition
 1.) Make a table of a few (the book uses seven) values of x, and corresponding values of y.2.) Plot the points and draw a smooth curve through them
Term
 Define (a^(1/n))^n
Definition
 (a^(n/n))= a^1
Term
 If rsubscrpt1, rsubscrpt2, rsubscrpt3, etc leads to r...
Definition
 Then a^rsubscrpt1, a^rsubscrpt2, etc leads to a^r
Term
 a^(1/n)
Definition
 nroot a
Term
 a cannot be...
Definition
 1,0, or less than 0
Term
Definition
 Is an increasing function
Term
 When a is greater than zero and less than 1, or a^(-x), then...[Exponential Decay]
Definition
 the graph of the curve is reflected across the x-axis
Term
 f(-x)
Definition
 Is a reflection about the y-axis
Term
 When the absolute value of a is less than one...
Definition
 Then you have a horizontal stretch when..af(x)
Term
 The parent graph of an exponential function always hits the y-axis at...
Definition
 Point (0,1)
Term
 To find y-intercepts...
Definition
 1.) Set x=02.) Solve
Term
 Exponential functions have horizontal asymptotes but not....
Definition
 Vertical or Oblique Asymptotes
Term
 How do you find f(x), when given two points?
Definition
 1.) Think of it as f(x)=Ca^x, in which C is your constant.2.) If one of your points is (0,1), then that point represents your constant in the form f(0)=1.3.) With that knowledge you can say that your other point explains the function, so let's say that the other point is (2,16). That would mean your function is f(2)=16, which means a^2=16 which means that a=4.4.) And that is Your Answer
Term
 g(x)=e^x, in which e is defined as[Natural Exponential Function]
Definition
 The horizontal asymptote of f(x)
Term
 Continuous Compound Interest Formula
Definition
 A=Pe^(r+t)
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