p4, p5, p6

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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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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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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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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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line given linear information.Situation: A point and a slope.


passing through (-2, 3) with aslope of 4.

Easier because slope is alr eadygiven! Just f ind b.

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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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line given linear information.Practice:


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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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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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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Exponents and Radicals:

They ar e r elated. Cousins

maybe.

Law Example

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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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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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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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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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of a basic f unction.

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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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of a basic f unction.

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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.

p4, p5, p6

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