graphsgraphs 100 50 25 10 5 power functions polynomialspolynomials rational functions miscmisc math...
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![Page 1: GraphsGraphs 100 50 25 10 5 Power Functions PolynomialsPolynomials Rational Functions MiscMisc Math 104 – Test 1 Review 100 50 25 10 5 100 50 25 10 5](https://reader036.vdocuments.us/reader036/viewer/2022062320/56649d6a5503460f94a48595/html5/thumbnails/1.jpg)
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![Page 2: GraphsGraphs 100 50 25 10 5 Power Functions PolynomialsPolynomials Rational Functions MiscMisc Math 104 – Test 1 Review 100 50 25 10 5 100 50 25 10 5](https://reader036.vdocuments.us/reader036/viewer/2022062320/56649d6a5503460f94a48595/html5/thumbnails/2.jpg)
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?
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It will be chair It will be chair shaped.shaped.
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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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At x = 50.At x = 50.
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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
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xx
![Page 8: GraphsGraphs 100 50 25 10 5 Power Functions PolynomialsPolynomials Rational Functions MiscMisc Math 104 – Test 1 Review 100 50 25 10 5 100 50 25 10 5](https://reader036.vdocuments.us/reader036/viewer/2022062320/56649d6a5503460f94a48595/html5/thumbnails/8.jpg)
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
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![Page 10: GraphsGraphs 100 50 25 10 5 Power Functions PolynomialsPolynomials Rational Functions MiscMisc Math 104 – Test 1 Review 100 50 25 10 5 100 50 25 10 5](https://reader036.vdocuments.us/reader036/viewer/2022062320/56649d6a5503460f94a48595/html5/thumbnails/10.jpg)
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xx -3 -3
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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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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
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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?
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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
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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?
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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.
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(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?
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Rational Functions
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What is the horizontal asymptote of What is the horizontal asymptote of
63
3)(
x
xxf
Y=1/3Y=1/3
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Find all vertical asymptotes of the Find all vertical asymptotes of the functionfunction
65)(
2
xx
xxg
x=2 and x=3x=2 and x=3
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2
3)(
x
xxh
Sketch the graph of the functionSketch the graph of the function
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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
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Miscellaneous
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The Gators The Gators
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What is the GRCC mascot?What is the GRCC mascot?
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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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What is the name of the school What is the name of the school newspaper?newspaper?
The CurrentThe Current
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SMT 340SMT 340
What room are you in? What room are you in?
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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)?