Economics 214
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Transcript of Economics 214
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Economics 214
Lecture 9
Intro to Functions Continued
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Power function when p is positive odd integer
If k>0, then the function is monotonic and increasing. If k<0, then the function is monotonic and decreasing.
If p≠1 and k>0, the function is strictly concave for x<0 and strictly convex for x>0.
If p≠1 and k<0, the function is strictly convex for x<0 and strictly concave for x<0.
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Figure 2.14 Power Functions in Which the Exponent Is a Positive Odd Integer
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Power function with p negative integer
The function is non-monotonic The function is not continuous and has
a vertical asymptote at x=0.
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Power function with p negative integer
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Power function with p negative integer
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Figure 2.15 Power Functions in Which the Exponent Is a Negative Integer
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Polynomial Functions
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Polynomial Functions
The degree of the polynomial is the value taken by the highest exponent.
A linear function is polynomial of degree 1.
A polynomial of degree 2 is called a quadratic function.
A polynomial of degree 3 is called a cubic function.
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Roots of Polynomial Function
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3 cases for roots of quadratic function
b2-4ac>0, two distinct roots. b2-4ac=0, two equal roots b2-4ac<0, two complex roots
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Quadratic example
34
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2*2
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xxy
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Plot of our Quadratic function
Roots of Quadratic Equation
-4
-2
0
2
4
6
8
10
12
14
-2 -1 0 1 2 3 4 5
x
y y
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Exponential Functions
The argument of an exponential function appears as an exponent.
Y=f(x)=kbx
k is a constant and b, called the base, is a positive number.
f(0)=kb0=k
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Exponential Functions
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Figure 2.16 Some Exponential Functions
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Exponential functions with k<0
Exponential Functions with k<0, b=3/2 and 2/3
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-6000
-5000
-4000
-3000
-2000
-1000
0
1000
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