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anonymous

  • 5 years ago

Summarize all pertinent information and sketch the graph of y = f(x): f(x) = sqrt (25-x^2)

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  1. anonymous
    • 5 years ago
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    Anyone there?

  2. anonymous
    • 5 years ago
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    Well, so what is pertinent? Your square root argument must not be negative, which restricts your domain

  3. anonymous
    • 5 years ago
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    so -5<=x<=5

  4. anonymous
    • 5 years ago
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    Next, how does that restrict the domain? x^2 is always positive, so the biggest the square root part can be is 5, and the smallest is 0, so the range is 0<=y<=5

  5. anonymous
    • 5 years ago
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    I don't know what your teacher means by "pertinent information," but you can graph from there.

  6. anonymous
    • 5 years ago
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    Square both sides of the equation y=(25-x^2) and rearrange the terms as shown below: \[y^2 + x^2=5^2\] I might be wrong but isn't that a circle, centered at the origin with a radius of 5?

  7. anonymous
    • 5 years ago
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    but the circle is not a function. You often can't just square both sides when it is a function. If the f(x) was really a y, then yes, it is a circle radius 5

  8. anonymous
    • 5 years ago
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    What we actually get looks to be the top half of that circle

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