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Do Now
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Objectives P4, P5, P6Honor s Calculus
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Agenda
1. Discuss Do Now (5 min)
2. Homework Questions (10 min)
3. OBJ P4
4. OBJ P5
5. OBJ P6
6. Star t Homework
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Do Now Review
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P4: Determine the equation of a
line given linear information.When looking to determine the equation of a line, we need 2
impor tant pieces of information:
1. Slope (m)
2. Inter cept (b)
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P4: Determine the equation of a
line given linear information.With those 2 pieces, you canwr ite an equation for any line.
The strategy is about how to f indthat information.
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P4: Determine the equation of a
line given linear information.Situations that may be encounter ed:
1. 2 points only.
2. A point and the slope.
3. A point and another line to
compar e to (parallel or
perpendicular).
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P4: Determine the equation of a
line given linear information.Situation: 2 points only.
Find the equation of the line
passing through (1, 3) and (5, 2).
Fir st, f ind the slope, then use
one of the points to f ind the inter cept.
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P4: Determine the equation of a
line given linear information.Situation: A point and a slope.
Find the equation of the line
passing through (-2, 3) with aslope of 4.
Easier because slope is alr eadygiven! Just f ind b.
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P4: Determine the equation of a
line given linear information.Situation: A point and another line to compar e to.
Find the equation of the line passing through (2, -2) that is
perpendicular to y=2x-1.
Find the slope using the slope of
the given line. Then f ind b.
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P4: Determine the equation of a
line given linear information.Practice:
Find the equation of the line
passing through the points (2, 1)and (-3, 5).
Then f ind the line parallel to that passing through (10, 4).
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P4: Determine the equation of a
line given linear information.Summary:
Fir st f ind slope, then f ind
inter cept.
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P5: Simplify complex f unctions
including radicals and exponentials.
We will be encounter ing all types of complex f unctions in calculus,
so we need to be eff icient and
accurate with simplif ication.
Let¶s r eview needed pr inciples«
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P5: Simplify complex f unctions
including radicals and exponentials.
Exponent Laws:Law Example
x1 = x 61 = 6
x0 = 1 70 = 1
x-1 = 1/x 4-1 = 1/4
xmxn = xm+n x2x3 = x2+3 = x5
xm/xn = xm-n x6/x2 = x6-2 = x4
(xm)n = xmn (x2)3 = x2×3 = x6
(xy)n = xnyn (xy)3 = x3y3
(x/y)n = xn/yn (x/y)2 = x2 / y2
x-n = 1/xn x-3 = 1/x3
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P5: Simplify complex f unctions
including radicals and exponentials.
Exponents and Radicals:
They ar e r elated. Cousins
maybe.
Law Example
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P5: Simplify complex f unctions
including radicals and exponentials.
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P5: Simplify complex f unctions
including radicals and exponentials.
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P5: Simplify complex f unctions
including radicals and exponentials.
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P5: Simplify complex f unctions
including radicals and exponentials.
Ther e will also be manypolynomials we need to simplify.
If you get a dr eadf ul, massive polynomial, the strategy is to
F ACTOR!
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P5: Simplify complex f unctions
including radicals and exponentials.
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P5: Simplify complex f unctions
including radicals and exponentials.
Summary:
Simplif ication laws ar e needed
in calculus to make problems
easier.
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P6: Determine the asymptotes
of a basic f unction. Asymptotes ar e signif icant incalculus. In fact, their very
def inition comes from calculus.
The def inition you learned in
Pr e-Calc was the ³unoff icial´
ver sion.
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P6: Determine the asymptotes
of a basic f unction. Asymptotes ar e ³boundar ies´ onthe graph that ³guide´ the
behavior of a line.
The off icial def inition will come
when we get to Limits!
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P6: Determine the asymptotes
of a basic f unction.Finding a ver tical asymptote:
Basically, look for something x
cannot ever equal.
A big clue: you can¶t have 0 in
the denominator.
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P6: Determine the asymptotes
of a basic f unction.
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P6: Determine the asymptotes
of a basic f unction.Finding a hor izontal asymptote:
This can be tr ickier, but not too
bad!
BOBO BOTN E ATS DC!
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P6: Determine the asymptotes
of a basic f unction.
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P6: Determine the asymptotes
of a basic f unction.Summary:
Asymptotes ar e guide to help
you graph.
BOBO BOTN E ATS DC!
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Questions?
HW: Problem Set P4-P6.