Agenda:
- Return of the Shadow
- Go over Homework 10 & 11
- Rational Functions
We had previously established that in order to solve this problem, we would use a pair of similar triangles from a diagram of the situation. We also found that as the height of the person increases, the shadow length does as well (i.e. height and shadow length are directly proportional.)
Next we set up proportions of the similar triangles to find the length of the shadow.
20/h= 12 + l / l (cross multiply. *note, cross multiplication can only be used when there
is an = sign!)
20l = h(12+l) (distribute the h)
20l = 12h+hl (subtract hl)
20l – hl = 12h (rearrange the equation into an equivalent situation)
l (20-h) = 12h --> l = 12h / 20-h (yay!!)
Domain Restrictions
Set of all x’s (inputs) that make sense in the function.
i.e. h cannot equal 20
h must be greater than or equal to 0
h must be less than 20
" 1 / damn big = damn small" -Carl Hostnik
Then we went over Homework 10 and reviewed asymptotes. We discovered that horozontal asymptotes can exist as well.
We reviewed Homework 11 next. We talked about an equation that applies to the homework and came up with two equivalent equations:
y = 100 / 4 - (100/x) and y= 100x / 4x-100
A horozontal asymptote occurs in this graph, as x gets really big, y gets closer to 25.
Last, we talked about Rational Functions!
- f(x) = P(x) / Q(x)
- P(x) and Q(x) are polynomial
- y= x*x+3x+4, or y= 4 / 9x
- a series of terms with a variable to a power of a whole number
We worked on some algebra, reviewing how to add/subtract, multiply and divide fractions.
Remember!
- Common denominator when adding/subtracting
- Multiply across
- Stay, dot, flop when dividing
Last, we worked on factoring rational functions.
ex. (x+3 / 7) * (14 / 2x+ 6) *2x+6 can be factored into 2(x+3)
2 * (x+3 / 7) * (14 / 2*x+3) = 1
- Next Scribe: ClaireH
- Homework: Practice Rational Functions worksheet, numbers 39-49 odds
- Quiz next Wednesday!!! Study!!
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