graphsgraphs 100 50 25 10 5 power functions polynomialspolynomials rational functions miscmisc math...

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Power Power FunctionsFunctionsPolynomialPolynomial

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FunctionsFunctionsRational Rational

FunctionsFunctionsMiscMiscMiscMisc

Math 104 – Test 1 ReviewMath 104 – Test 1 Review

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Graphs

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Y=-3xY=-3x33

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5 Point Question5 Point Question

In the long run, what power function will In the long run, what power function will the graph of y=-3xthe graph of y=-3x3 3 - 2x- 2x2 2 + 5 look like?+ 5 look like?

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What will the graph of y = (x+2)(x-3)What will the graph of y = (x+2)(x-3)33 look like right near x = 3?look like right near x = 3?

10 Point Question10 Point Question

It will be chair It will be chair shaped.shaped.

Which class of power functions all have Which class of power functions all have vertical asymptotes at x = 0?vertical asymptotes at x = 0?

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Y=kxY=kxpp, where p is , where p is negative.negative.

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25 Point Question25 Point Question

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At x = 50.At x = 50.

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50 Point Question50 Point Question

When does the graph of y = xWhen does the graph of y = x44 catch up with y = 50xcatch up with y = 50x33??

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As x-> +/-As x-> +/-, y -> -, y -> -33

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Describe the long-run behavior of the Describe the long-run behavior of the rational function rational function

100 Point Question100 Point Question

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Power Functions

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xx33, x, x22, x, x0.50.5, x, x-2-2, x, x-3-3

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When x>1, rank the following When x>1, rank the following from largest to smallest: from largest to smallest:

xx22, x, x33, x , x -2-2, x , x -3-3,x,x0.50.5

5 Point Question5 Point Question

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xx -3 -3

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10 Point Question10 Point Question

Which of these is biggest when Which of these is biggest when 0<x<1?0<x<1?

xx-2-2, x , x -3-3, x, x22, x, x1/21/2, x, x1/31/3

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Y=3xY=3x1/21/2

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25 Point Question25 Point Question

Find the equation for the power Find the equation for the power function passing through (1,3) and function passing through (1,3) and

(4,6).(4,6).

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Find the equation for an exponential Find the equation for an exponential function with the properties f(1) = 16 function with the properties f(1) = 16

and f(4) = 128and f(4) = 128

50 Point Question50 Point Question

F(x) = 8(2F(x) = 8(2xx))

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Readership is reduced by 42.2%Readership is reduced by 42.2%

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The number of people who read a The number of people who read a government report varies inversely with the government report varies inversely with the square root of the thickness of the report. square root of the thickness of the report. What effect does tripling the length of the What effect does tripling the length of the report have on the number of readers?report have on the number of readers?

100 Point Question100 Point Question

Polynomials

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44

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What degree is the What degree is the polynomial polynomial

y=-2(x+3)(x-5)(x-6)y=-2(x+3)(x-5)(x-6)22

5 Point Question5 Point Question

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What is the maximum What is the maximum number of turning number of turning

points y = -5xpoints y = -5x44+3x+3x33--2x2x22+5x+1 can have? +5x+1 can have?

10 Point Question10 Point Question

33

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Sketch the graph of y = -2(x+3)(x-4)(x-5), Sketch the graph of y = -2(x+3)(x-4)(x-5), labeling all intercepts.labeling all intercepts.

25 Point Question25 Point Question

(0,-120)(0,-120)

(4,0)(4,0) (5,0)(5,0)(-3,0)(-3,0)

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Y=2(x+1)(x-2) Y=2(x+1)(x-2) 22 (x-4) (x-4)

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Find a possible equation for the polynomial Find a possible equation for the polynomial graphed below.graphed below.

50 Point Question50 Point Question

(0,-32)(0,-32)

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aan n is negative is negative and n is oddand n is odd

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The graph of the polynomial The graph of the polynomial f(x) = af(x) = annxxnn+a+an-1n-1xxn-1n-1+…+a+…+a11x+ax+a00 falls to falls to

the right and rises to the left. What do the right and rises to the left. What do we know about the function?we know about the function?

100 Point Question100 Point Question

Rational Functions

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5 Point Question5 Point Question

What is the horizontal asymptote of What is the horizontal asymptote of

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Y=1/3Y=1/3

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10 Point Question10 Point Question

Find all vertical asymptotes of the Find all vertical asymptotes of the functionfunction

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x=2 and x=3x=2 and x=3

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25 Point Question25 Point Question

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Sketch the graph of the functionSketch the graph of the function

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50 Point Question50 Point Question

A chemist is studying how the A chemist is studying how the concentration of tin in an alloy affects concentration of tin in an alloy affects the conductivity of the alloy. The the conductivity of the alloy. The chemist starts with 5 g of copper and chemist starts with 5 g of copper and adds tin to the alloy. Express the adds tin to the alloy. Express the concentration of tin as a function of how concentration of tin as a function of how much tin is added. much tin is added. C(x)=x/(x+5) C(x)=x/(x+5)

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100 Point Question100 Point Question

Find a possible formula for the function Find a possible formula for the function graphed below.graphed below.

F(x)=(x+3)(x-1)/(x-4)F(x)=(x+3)(x-1)/(x-4)22

Miscellaneous

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The Gators The Gators

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What is the GRCC mascot?What is the GRCC mascot?

5 Point Question5 Point Question

What is the name of the tall white What is the name of the tall white pointy building in Seattle with a round pointy building in Seattle with a round rotating disk at the top?rotating disk at the top?

The Space NeedleThe Space Needle

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10 Point Question10 Point Question

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25 Point Question25 Point Question

What is the name of the school What is the name of the school newspaper?newspaper?

The CurrentThe Current

SMT 340SMT 340

What room are you in? What room are you in?

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50 Point Question50 Point Question

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FINAL JEAPORDYFINAL JEAPORDY

It is symmetrical It is symmetrical about the y-axis.about the y-axis.

If f(-x) = f(x), what do we know about If f(-x) = f(x), what do we know about the graph of f(x)?the graph of f(x)?