Key Notes for Domain and Range: Domain is the x values, Range is the y. When Finding domain, go across horizontally to see how far the graph is stretching. What values of x does it hit? For the range, go up and down vertically to see how far the graph stretches. What values of y does it hit?
Key Notes for End Behavior: End behavior is simply looking at what is happening at the end points of the graph: As x --> infinity, what is y doing? If the y values are increasing as x is increasing, y is --> infinity. If they are decreasing, y --> negative infinity. As x --> negative infinity, what is y doing? if the y values are increasing, y --> infinity. If they are decreasing, y --> negative infinity.
Key notes for Increasing and Decreasing: Think of your slopes: when you have a positive slope (going up a hill or roller coaster) your graph is increasing. When you have a negative slope (going down a hill or roller coaster) your graph is decreasing. Sometimes, with lines like a linear function, the graph is only increasing or decreasing- its not doing both. Additionally, with increasing and decreasing, you are reading LEFT to right across the x axis. So when identifying the points that it is increasing and decreasing from, you are identifying it for the x value, not the y
IF, after watching the videos and doing some practice problems the above areas are still a problem area for you, search for, and watch, other videos until you find one where the explanation clicks. Don't make this material harder than it has to be!
When asked to "determine algebraically" whether a function is even or odd, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f(–x) =f(x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f(–x) =–f(x), so all of the "plus" signs become "minus" signs, and vice versa), then the function is odd. In all other cases, the function is "neither even nor odd".
Example: Determine algebraically whether f(x) = –3x2 + 4 is even, odd, or neither.
When looking at a graph, look for symmetry to indicate if it is even or odd. If its symmetrical ACROSS THE Y-AXIS, its even. If it is symmetrical over the origin (meaning if I rotate it 180 degrees, it looks the same), it is odd. If there is no symmetry per above criteria, it is neither.
Note: the below Unit 3 review is for transformations & Graphs. It does not include the growth/decay, variation or solving exponentials (logs) portion of the test. Additionally #13e and #18 are exponential questions- you can skip those.