Understand that an inverse function is the reflection of the original function

Understand that an inverse function is the reflection

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and that this is necessary in order to be able to find an inverse function. Understand that an inverse function is the reflection of the original function around the line x y , and that cancellation laws state that if we apply the original function and the inverse function in succession, we get back the original x value we started with. Know how to find an inverse function by solving for x in ) ( x f y and then switching x and y . Know that the domain of the inverse is the range of the original function, and vice versa. Finally, regarding inverse trig, know what we mean when we say e.g. 2 1 sin 1 …the point is, we’re looking for the angle whose sine is ½ . (don’t forget we work with radians in this course!) Know the restricted domains for sine, cosine, and tangent, and hence, be able to apply the cancellation laws. Lastly, if you are given something like e.g. ) sin(cos 1 x , or 5 3 cos sin 1 , then know that you need to set up a triangle with cosine (think SOHCAHTOA) of x , or 3/5 respectively in this case, and finally, find sine for this triangle. Really not as bad as you think…just practice! 1.5: Exponential and Logarithmic Functions First of all, you should have an understanding of what the exponential function is, and how to sketch its graph; similarly, you should be familiar with the natural exponential function, x e , which is a very important special case. You should also be familiar with how to apply exponent laws, and how to set up and solve application problems (e.g. population growth, half-life, etc). You should also have an understanding of what the logarithmic function is, and how to sketch its graph; similarly, you should be familiar with the natural logarithm function, ) ln( x , which is a very important special case (base e ). You should also be familiar with how to apply properties of logarithms to simplify them. Next, know the cancellation laws which arise because logarithmic functions and exponential functions are inverse functions (one undoes the other), and how to apply this to solve for x in equations involving logarithms or exponentials (including application problems).
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2.1: A Preview of Calculus All you should really know from this section for now is the basic concept…the limit of the secant lines as the point Q gets closer to P gives us the tangent line…we’ll study this more formally once we get to derivatives. 2.2: The Limit of a Function Understand what it means to find the limit of a function. Know how to find the limit graphically and numerically. To find limits numerically, you’re just substituting in values of x close to the one at which you want to find the limit. Understand the idea of finding limits from the left and right, and that for the limit at a point to exist, the limits from the left and right must be equal. Be able to determine if a function has a limit of positive or negative infinity, and hence find vertical asymptotes.
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