Calculus I: Write 120-150 words Definition paragrapghs with at least one example

Garcia & Low 1 Anabel Garcia & Judy Low Mrs. Pirraglia Calculus I 6 December 2015 Writing to Define DOMAIN The domain of a function is a set that represents all p ossible input values. Sometimes the domain will be all real numbers (like for polynomial and trig onometric functions) , but other times some values will need to be excluded. Findin g the domain is usually easier when we try to figure out if any numbers cause a problem for the function . It’s like being lactose intolerant and asking your doctor about a good diet . Instead of naming every food item that is okay , it makes more sense for the doctor to identify the few things that will make you sorry if you do eat them. This is related to (but not the same as) the range of function, which instead is the set of resulting output values. Some examples: ()= 4− 32+ 9− 1 The domain of a polynomial is all real numbers. ()= 5− 11 + 4 (− 3)(2− 1) The domain is {|≠ 3,≠ 1 2}. The denominator equals zero for these -values so the rational function is undefined there. ℎ()= log 3 The domain is {|> 0}. Since log and exponential functions are inverses, it makes sense that if the output of an exponential function is always positive, then the input of the logarithmic function must also always be positive. Garcia & Low 2 SYMMETRY The symme try of a function is a property which describes how the graph may be reflected onto itself. An even function is symmetric about the -axis, so the -axis acts like a mirror where the left side looks like a reflection of the right side and vice versa . Als o, if the paper is folded along the -axis, the left and right sides will meet. An odd function is symmetric about the origin, and this graph looks the same if you spin the paper around 180 o and look at it upside down. Even though symmetry describes wh at the graph looks like, we use algebra to test for this property. If ()= (−), the graph is even and so it is symmetric about the -axis. I f (−)= −(), the graph is odd and so it is symmetric about the origin. Some examples: ()= 6− 34+ 12 Since (−)= (−)6− 3(−)4+ 12 = 6− 34+ 12 = (), the function is even. While not all even functions are polynomial or even rational functions, notice that in this polynomial all th e exponents are even. ()= 6+ 2 83 Here, (−)= (−)6+2 8(−)3 = 6+2 8(−3)= − 6+2 83 = −(), so the function is odd. Note that we can rewrite () as ()= 6 83+ 2 83= 1 83+ 1 43 so that we see the odd powers more easily.