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Anonymous asked in Science & MathematicsMathematics · 9 years ago

10 points! explain work graphing square root and cube root functions?

10 points! explain work graphing square root and cube root functions?

GRAPH THE FUNCTION. EXPLAIN HOW THE GRAPH IS DIFFERENT THAN THE PARENT FUNCTION. THEN STATE THE DOMAIN AND RANGE.

1. y=∛x-7

2. y=√x +6

3. y=-2√x-3

4. y=3∛x+4 -9

1 Answer

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  • 9 years ago
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    Hi,

    1. y=∛x-7

    For cube root functions, the domain and range are always all real numbers, (-∞,∞).

    When x = 0, then y = -7. When x = 1, then y = -6. when x = -1, then y = -8. When x = 8, then y = -5. When x = -8, then y = -9. This shows the entire graph has been shifted down 7 from the parent graph.

    2. y=√x +6

    To find the domain on square root functions, always make the expression inside the radical greater than or equal to zero, and solve this.

    x ≥ 0 is the domain, so it is [0,∞).

    When x = 0, then y = 6. When x = 1, then y = 7. When x = 4 then y = 8. This shows that the y value starts at 6 and then continues to increase, So the range is [6,∞).

    This graph was shifted up 6 from its parent function.

    . . . . . . ___

    3. y= -2√x-3

    If x - 3 is all inside the radical, then make the expression inside the radical greater than or equal to zero, and solve this.

    x - 3 ≥ 0, then x ≥ 3 is the domain, so it is [3,∞).

    When x = 3, then y = 0. When x = 4, then y = -2. When x = 7 then y = -4. This shows that the y value starts at 0 and then continues to decrease, So the range is (-∞,0].

    This graph was shifted 3 squares to the right, is then flipped over the x axis to go down instead of up because of the -2 in front of the radical, and its y values change twice as fast as they do on the parent function.

    4. y=3∛x+4 -9

    For cube root functions, the domain and range are always all real numbers, (-∞,∞).

    If you set the expression inside the radical equal to zero, it gives the horizontal shift from the parent function. Then the number added or subtracted outside the radical gives the vertical shift from the parent function.

    The y values will also increase 3 times as fast because of the 3 in front of the radical.

    Since x + 4 = 0 solves to x = -4 and the constant as the separate term outside the radical is -9, then the point at (0,0) on the parent function is moved to (-4,-9). The points (1,1) and (-1,-1) on the parent function are relocated to (-3,-6) and (-5,-12) respectively. The points (8,2) and (-8,-2) on the parent function are relocated to (4,-3) and (-12,-15) respectively.

    I hope that helps!! :-)

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