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Given the function k(x) = x2, compare and contrast how the application of a constant, c, affects the graph. The application of the constant must be discussed in the following manners:

k(x + c)
k(x) + c
c • k(x)

  • math -

    shift or scale. Any ideas which go where?

  • math -

    i don't understand it can you

  • math -

    consider the graph

    k(x) = x^2

    k(x) = x^2+5 is the same graph, shifted up 5 units.

    Similarly, k(x) = (x-5)^2 is the same graph, shifted to the right by 5 units.

    If you think of the k-axis moved to the right 5 units, all the new x-coordinates are 5 less than the old ones. That's why substituting (x-5) is the same as moving the k-axis 5 units to the right.

    Think of scaling the same way. The graph grows or shrinks because the x-coordinate grows or shrinks by a factor of c.

    Visit where you can play around with tweaking the functions and see how they are affected. You can display up to 3 graphs at once. So, enter

    x^2 for the first,
    (x-5)^2 for the 2nd, and
    x^2+5 for the 3rd.

    You might want to change x and y ranges from -5 to 5 and make them -10 to 10 instead. Just play around some.

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