Unit 1 Day 1 NotesDomain, Range, Functions, Max, Min, Vertex, End Behavior, Intercepts, Interval N August 26, 2014
Welcome to Math III with Mrs. Higgins Please find your assigned seat. If you do not have a seat, please stand at the back by the white board.
1. Given: State the slope and the yintercept. 2. Graph a parabola with a vertex at (2, 3) facing up.
Please take out a clean sheet of notebook paper and a pencil. In the upper right hand corner, above the blue lines, please write your name, date (8/25/14), and the period. On the top blue line, please write WarmUp for 8/25. Copy each problem down and show all work to complete the problem.
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3. Factor completely: 2x2 +7x+6 4. Solve for x: 3(2x1)=105x
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5. If the measure of angle 3 is 70 degrees, what is the measure of angle 6?
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Unit 1 Day 1 Notes: Relations, Functions and Parts of a Graph Example 1) What are the domain and range of this relation? {(4,0), (3,1), (0,2), (1,2), (3,3)}
~Relation: a pairing of any two sets of numbers ~Function: a pairing of two sets of numbers in which the first value
Domain:
never repeats; passes the vertical line test ~Domain: the set of all possible xvalues ~Range: the set of all possible yvalues
Range: Is this a function? Why or why not?
remember to always use set notation if listing, write from least to greatest and do not repeat values.
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Unit 1 Day 1 NotesDomain, Range, Functions, Max, Min, Vertex, End Behavior, Intercepts, Interval N August 26, 2014 Evaluating A Function What does it mean to "evaluate" a function?
What does the answer represent?
Example 2) Is this a function? Why or why not?
***be sure to use parenthesis when substituting...it makes a significant difference in some problems!!!! Ex
right here...w/o parenthesis, many students would have made a mistake...be careful!!!!
This was just an extension to see if we could come up with the proper domain from this picture.
The next example is for Honors ONLY!!!!
If we substitute an expression instead of a numeric value, our Aug 2411:51 PM
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answer is highly likely to be an expression as well.
Determine if the Equation is a Function Ex Evaluate the function and write as an ordered pair. A.
, for
B.
* If y is in absolute value bars, not a function.
, for
* If y is to an even power, not a function. Example 5) State whether the following equations are functions: y = x2 + 2
b.
x = y2 – 3y
c.
y = 3x
Don't let the x as an exponent freak you out! Remember that we only care about the y variable in this type of question!
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Unit 1 Day 1 NotesDomain, Range, Functions, Max, Min, Vertex, End Behavior, Intercepts, Interval N August 26, 2014
Interval Notation – an alternative way of expressing an inequality Symbols:
Reworking what we know... Inequality
Picture
Interval Notation
2 < x < 6 3 < x < 0
to er r. d in e *if you would use a less than or m rit ss re t w gue a a greater than symbol for an inequality, t t s ne to ju a ve 've l ge ct. use a parenthesis for interval notation. l e u a i b I h yo w rre *if you would use a less than or equal to If at n it nco wh ritte ed i or a greater than or equal to for an inequality, w k ar m use a square bracket. [ or ]
x > 5 x < 2 All real numbers
*the infinity signs ALWAYS take a parenthesis as infinity is not a value we can EQUAL. *remember if using interval notation, we have to train our eye NOT to read something in parenthesis as an ordered pair.
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Intercepts
End Behavior
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Unit 1 Day 1 NotesDomain, Range, Functions, Max, Min, Vertex, End Behavior, Intercepts, Interval N August 26, 2014 Extrema (include vertex)
Extrema are the maximums and minimums of the graph.
There are two categories of extrema: local/relative and absolute. A curve may have multiple relative extrema. A curve may not have absolute extrema, may have one kind and not the other.
Extrema are written either as a complete ordered pair, or as just the yvalue.
Ex State the following:
Intervals of increasing, decreasing & constant *use interval (honors/cp) or inequality (cp) notation *represents the span of the xaxis where an idea is *endpoints are NEVER included!!!!!!!
Ex State the interval(s) for increasing, decreasing and constant.
Inc:
dec:
relative max(s):
Constant:
relative min(s):
absolute max(s):
absolute min(s):
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