Summarize the following:
Oftentimes, it is easiest to determine the range of a function by simply graphing it. Many root functions have a range of (-∞, 0] or [0, +∞) because the vertex of the sideways parabola is on the horizontal, x-axis. In this case, the function encompasses all of the positive y-values if the parabola goes up, or all of the negative y-values if the parabola goes down. Fraction functions will have asymptotes that define the range.  Some root functions will start above or below the x-axis. In this case, the range is determined by the point the root function starts. If the parabola starts at y = -4 and goes up, then the range is [-4, +∞). The easiest way to graph a function is to use a graphing program or a graphing calculator. If you do not have a graphing calculator, you can draw a rough sketch of a graph by plugging x-values into the function and getting the corresponding y-values. Plot these coordinates on the graph to get an idea of the shape of the graph. Once you have graphed the function, you should be able to clearly see the lowest point of the graph. If there is no obvious minimum, know that some functions will continue on to -∞. A fraction function will include all points except those at the asymptote. They often have ranges such as (-∞, 6) U (6, ∞). Again, after graphing, you should be able to identify the maximum point of the function. Some functions will continue on to +∞ and therefore, will not have a maximum. Like the domain, the range is written with the same notation. Use a bracket when the number is included in the domain and use a parenthesis when the domain does not include the number. The letter U indicates a union that connects parts of a domain that may be separated by a gap.  For example, a range of [-2, 10) U (10, 2] includes -2 and 2, but does not include number 10. Always use parentheses if you are a using the infinity symbol, ∞.

summary: Graph the function. Find the minimum of the function. Determine the maximum of the function. Write the range with proper notation.


Summarize the following:
In a pot on the stove, hard boil two eggs. After the two eggs have boiled, remove the eggs from the water and let them cool. Letting the eggs cool before you make the egg salad will help the eggs be firmer and easier to chop. Run the eggs under cold water to speed up cooling. After the eggs have cooled, peel them, then chop them into small pieces. Use a sharp knife and try to cut make the cubes of egg equal sizes so that the texture of the egg salad is consistent. Place the chopped boiled eggs in a medium mixing bowl and gradually add the mayonnaise, mixing continuously. Keep adding the mayonnaise until you are satisfied with the consistency. Add the mustard and relish and stir to combine all of the ingredients. Taste the egg salad and add more salt, pepper or other condiments like hot sauce or red wine vinegar as you wish. If you want your bread to be toasted and crispy, place the two pieces of toast in the toaster. If you don’t want your bread to be toasted, leave the bread as is. Spoon the egg salad onto one piece of bread, then place the other piece of bread on top. Slice the sandwich in half and enjoy!  If you want the egg salad to be cold, store it in the fridge for an hour or so, then make the sandwich. Lettuce and tomato taste great on an egg salad sandwich!

summary: Hard boil two eggs. Chop the boiled eggs. Mix in the mayonnaise. Mix in the mustard and relish. Toast the bread. Put the sandwich together.


Summarize the following:
Use an over the counter pain reliever medication, such as ibuprofen or naproxen sodium. The medication will ease the discomfort caused by the sunburn while your lips heal.  Use pain relievers according to their package instructions. Do not overdose. Even over-the-counter pain relievers may interact with prescription drugs or other medications. If you are currently taking any other medications, ask your doctor about which pain relievers are safe for you. Take a clean cloth and let it soak in a container of ice water for a few minutes. Wring out the excess water, then hold it to your lips for as long as the cloth stays cool. Doing this while your lips heal will provide some quick and simple relief. Steep some chamomile tea bags in hot water, then take them out and let them cool. Hold the bags directly to your lips for as long as they stay cool. Chamomile is a natural way to relieve pain from burns, so as long as the bags are cool, they’ll be effective on your sunburned lips.
summary: Take pain-relieving medication. Put on a cold compress. Relieve the pain with chamomile.