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This lesson is a basic discussion of the graphs of square root and cube root functions.
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When graphing the square root function, of the form  , remember that a square root with no sign in front of the square root symbol is assumed to be positive.
• The x-value in f (x), the radicand, can never be negative, since a negative number under the square root symbol is not a real number. The domain of this function is x > 0, or [0, ∞) as written in interval notation.
• The graph of will be increasing from left to right across the domain, with all y-values (in this functions) being positive (or zero).
The end behavior of this square root function:
f (x)
→ +∞, as x → +∞
f (x)
→ 0, as x → 0 from the right
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If a negation of a square root is to be examined, it will appear in the form  , with a negative sign in front of the radical.
• The graph of will be decreasing from left to right across the domain, x > 0, or [0, ∞), with all y-values (in this function) being negative (or zero).
The end behavior of this square root function:
f (x)
→ +∞, as x → -∞
f (x)
→ 0, as x → 0 from the right |
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The graph of 
shows a translation 4 units to the right. |
When working with cube roots, the cube root of a positive number is positive, and the cube root of a negative number is negative. Unlike the square root function, the domain of the cube root function is all real numbers. While the square root function must limit the value of x to be non-negative, the cube root function has no such limitation.
• Given the cube root function,  .
• The domain of this cube root function is all real numbers.
• This cube root function is increasing from left to right across the domain.
The end behavior of this cube root function:
f (x)
→ +∞, as x → +∞
f (x)
→ -∞, as x → -∞ |
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• Given the negation of a cube root function,  . • The domain of this negation of a cube root function
is all real numbers.
• The graph of is decreasing from left to right across the domain.
The end behavior of this cube root function:
f (x)
→ +∞, as x → -∞
f (x)
→ -∞, as x → +∞ |
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For
calculator help with graphing
radical functions.
click here. |
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