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Math Help - Discontinuity Graphs Homework Check

  1. #1
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    Sep 2012
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    Ny
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    Discontinuity Graphs Homework Check

    I think most of my answers are right but need confirmation



    The directions are to ....

    a) Make a sketch of the graph
    b) Represent any points of discontinuity with a hole
    c) Name domain and range
    d) Where appropriate, simplify and name new function


    __________________________________________________ ____________
    1. h(x) = sqrt(3x-4)
    a) upper half of sideways parabola infirst quad starting at x=4/3
    but i dont know what the y-value is
    b) no holes?
    c) D=[4/3,inf)
    R= ?
    d) cant be simplified
    __________________________________________________ ___________
    2. F(x)= (4x2-1)/(2x+1)
    a)line with positive slope with y int at -1
    b) hole at (-1/2,-2)
    c) D=(-inf,-1/2),(-1/2,inf)
    R=(-inf, -2), (-2,inf)
    d) new function = 2x-1
    __________________________________________________ _____________-
    3. f(x)=(x2-4x+3)/(x-1)
    a) line with positive slope with y-int at -3
    b) hole at (1,-2)
    c) D=(-inf, 1),(1,inf)
    R=(-inf,-2),(-2,inf)
    d) new function = x-3
    __________________________________________________ __________________
    4. This ones a piecewise function
    f(x)={2x-1 if x cant equal 2
    {0 if x=2
    a)line with y int at -1 and point at (2,0)
    b) hole at (2,3)
    c) D=all reals
    R=(-inf,3), (3,inf)
    d)cant be simplified
    __________________________________________________ _____________
    5. also a piecewise function
    h(x)={x+6 if x is less than or equal to -4
    {sqrt(16-x2) if -4<x<4
    {6-x if x is greater than or equal to 4
    a) semi circle in top half of graph with ends at 4 and -4 but open circles, one line with negative slope in second quad above x-axis at -4 and the same image flipped in other quad
    b) holes at (-4,0) and (4,0)
    c) D= all reals
    R=(-inf, 4)
    d) cant be simplified
    __________________________________________________ _____________________________________
    6. also piecewise function
    g(x)={x-2 if x<0
    {0 if x=0
    {x2+1 if x>0
    a)right side of parabola with open circle on y int, point at the origin, line with negative slope y-int at -2 as open circle
    b)holes at (0,1) and (-2,0)
    c) D=all reals
    R=(-inf,-2),[2,2],(1,inf)
    d) cant be simplified
    __________________________________________________ __________________________________________________ ___
    7. F(x)= (x3+3x2+x+3)/(x+3)
    a) parabola centered at origgin with hole at x-value of -3
    b) hole at (-3,10)
    c) D=(-inf, inf),(x cant equal -3)
    R= [0,inf), (y cant equal...10?)
    d) new function = x2+1
    __________________________________________________ _________________________________________-
    Thanks
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  2. #2
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    Sep 2012
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    Ny
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    Re: Discontinuity Graphs Homework Check

    This is due tomorrow and I really want to make sure my answers are correct so any help at all would be greatly appreciated
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