Rational and Exponential Functions

Kaitlyn L
Mind Map by Kaitlyn L, updated more than 1 year ago
Kaitlyn L
Created by Kaitlyn L about 5 years ago
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Mind map for Math 2 class
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Rational and Exponential Functions
1 Rational function
1.1 A function that is the ratio of two polynomials
1.1.1 This is a rational function because the denominator is divided by the numerator
2 Horizontal & Vertical Asymptotes of Rational Functions
2.1 Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function
2.1.1 1 is the vertical asymptote of the graph because in the donominator x minus 1 is zero so the denominator cannot be divided by the numerator which is one
2.1.1.1 Also on in the graph the graph approaches 1 on the x-axis but, does not touch it
2.2 Horizontal asymptotes are where the graph approaches a value across the y-axis but does not touch it
2.2.1 The horizontal asymptote of this graph is y=2
2.2.2 You can look at the domain to determine the horizontal asymptote
2.2.2.1 For example if the domain is all x-values other than ± 3/2, and the two vertical asymptotes are at x = ± 3/2.
3 Exponential function
3.1 function in which an independent variable appears in one of the exponents
3.1.1 y=ab^x
4 Horizontal Asymptotes of Exponential Functions
4.1 The horizontal asymptote is where the graph approaches a value across the y-axis but does not touch it
4.1.1 The number that is being added in the equation is the horizontal asymptote of the equations above
5 End behavior of a graph with asymptotes
5.1 the end is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity
5.1.1 The function on the right side increases and approaches infinity
5.1.1.1 The function on the left side decreases and approaches negative infinity
6 Y-intercept of an exponential function
6.1 The Y-intercept of an exponential function iswhere the function crosses the y-axis
6.1.1 The x value of a Y-intercept will always be zero so when x is zero the function crosses the y axis
6.1.1.1 The Y-intercept of this graph is (0,1)
7 Exponential growth function
7.1 The exponential growth function is k>0
7.1.1 In this function k is known as the growth factor
7.1.1.1 Growth factor is the factor by which a number multiplies itself over time
8 Exponential decay function
8.1 The exponential decay function is k<0
8.1.1 In this function k is known as the decay factor
8.1.1.1 Decay factor is the factor by which a number divides itself over time
9 Growth factor of an exponential function
9.1 When a > 0 and b > 1, the function models growth.
9.1.1 b is the growth factor and a is the initial amount
10 Decay factor of an exponential function
10.1 When a > 0 and 0 < b < 1, the function models decay
10.1.1 b is the growth factor and a is the initial amount
11 Compound Interest Formula
11.1 A represents amount of money accumulated after n years, including interest.
11.2 P represents principal amount (the initial amount you borrow or deposit)
11.3 r represents annual rate of interest (as a decimal)
11.4 n represents number of times the interest is compounded per year
11.5 t represents number of years the amount is deposited or borrowed for.
12 Continuous Compounding
12.1 A = amount after time t
12.1.1 P = principal amount (initial investment)
12.1.1.1 r = annual interest rate (as a decimal)
12.1.1.1.1 t = number of years
12.2 The continuous compound formula can be used to find the balance at the bank
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