MA 1165 - Lecture 03 1/21/09 Weve seen that if we have a quadratic function of the form f(x) = a(x d)2 + c,
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then we can tell what the graph is going to look like pretty easily. The a is a stretching and ipping factor, and the vertex will be at (d, c). N
MA 1165 - Lecture 15 02/23/09
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Right Triangles
A lot of what we do is based on the properties of a right triangle. In particular, most of the rest of the semester will be devoted to the trigonometric functions, which will be dened in terms of right tri
MA 1165 - Lecture 13 02/18/09
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The (positive) square root symbol
We've used the square root symbol already, but before we move on, I want to emphasize something about it. When we say 4, this specifically is the positive square root of 4, so 4 = 2. (1)
MA 1165 - Lecture 14 2/20/2009
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Solving Equations Involving Exponential Functions
We dened the logarithmic functions to be the inverses of the exponential functions. We can use the log functions, therefore, to solve equations involving the exponential
MA 1165 - Lecture 12 2/16/09
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Solving Equations.
Whenever you are solving an equation algebraically, you want to get x by itself on one side of the equation. In general, you want to perform a sequence of moves, which usually is doing the same thing to
MA 1165 - Lecture 11
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2/13/09
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Some Log Identities
loga (x) = (1)
In addition to the equation logb (x) , logb (a) which we've already used, here are a few more special formulas for logs that are useful. One is loga (x) + loga (y) = loga (xy), and this i
MA 1165 - Lecture 09 Wednesday, February 4, 2009
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Exponential Functions
f(x) = 2x . (1)
Consider the function This is an example of an exponential function. We have a constant in the base, and the variable x is an exponent. Exponents are based on the c
MA 1165 - Lecture 10 2/06/09
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Logarithmic Functions
f(x) = ax .
In the last class, we looked at exponential functions, which took the form (1)
It is useful to have a set of inverse functions for the exponential functions. We'll call these functions the
MA 1165 - Lecture 08
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Monday, February 2, 2009
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Middle Behavior of Power Functions with Negative Exponents
If you look back at the graphs of the power functions with negative exponents from last time, youll see that they all have an asymptote at x = 0 (
MA 1165 - Lecture 07
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Friday, 1/30/09
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Shapes of Power Functions with negative exponents
Like the power functions we looked at last time, the power functions with negative exponents have graphs with distinctive shapes and patterns. Specifically, these f
MA 1165 - Lecture 06
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Wednesday, 1/28/09
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Shapes of Power Functions
I would like you to be familiar with the shape of the power functions, that is, the functions of the form f(x) = xn , (1)
for n = 1, 2, 3, . . . Lets look at the graphs of the rst sever
MA 1165 - Lecture 02 Wednesday(1/14/09) and Friday (1/16/09)
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Quadratic Functions
f(x) = ax2 + bx + c.
A quadratic function is one that takes the form
The simplest quadratic function is f(x) = x2 , and its graph looks like the one shown in Figure 1.
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