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Math Help - Intercepts, domain and range?

  1. #1
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    Intercepts, domain and range?

    Let f(x) = {√x, 0 ≤ x ≤ 1
    { 1/x, x > 1

    (a). Identify any intercepts
    (b). Graph the function
    (c). Find the domain and range

    I'll be able to graph it, I just can't do a or c
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  2. #2
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    Quote Originally Posted by romanianxromo View Post
    Let f(x) = {√x, 0 ≤ x ≤ 1
    { 1/x, x > 1

    (a). Identify any intercepts
    (b). Graph the function
    (c). Find the domain and range

    I'll be able to graph it, I just can't do a or c
    Intercepts imply intercepting with the x-axis or y-axis.

    The function would intercept the y-axis at x = 0 which is for the first piece.

    \sqrt{0} = 0

    It's y-intercept is at x = 0.

    It's x-intercept is whenever y = 0. Notice that the x-intercept is the same as the y-intercept.

    The domain is all real numbers that can go into the function. The square root cannot take any negative values and the \frac{1}{x} cannot take zero, but it's not even a valid piece of the function in that region, so the domain is simply all non-negative reals. The range is just the same.
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  3. #3
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    Oh, ok. I see.

    So then how would I plug that into my TI 84 + to get the graph?

    Y1=(X and 0≤x≤1
    Y2=(1/x and x > 1

    I got a horizontal line at the point (0,1) is that right?
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