POWER MODELS

X^2

X^2 Table

X^2GRAPH

EXPERIMENT 1: Y=X^2

• Y-values are 0 are positive values
• U-shaped graph (parabola)
• Decreases at a decreasing rate(slows down)
• Increases at an increasing rate (speeds up)

Y=2X

Y=2X

Y=2X

Y=2X

• Exponent is 1
• Increasing line
• The Y values increase by two
• Linear equation

EXPERIMENT 2

2X^2

Y=2X^2

Y=2X^2

Y=3X^2

Y=3X^2

Y=3X^2

Y=5X^2

Y=5X^2

Y=5X^2

Y=2X^2,Y=3X^2,Y=5X^5

• U-shaped graph
• U shape got closer to quadrants
• Shape became more narrow

Y=(1/2)X^2

Y=(1/2)X^2

Y=(1/2)X^2

Y=(1/2)X^2

• U-shape got wider
• Farther from the Y-axis

Y=-1X^2

Y=-1X^2

Y=-1X^2

Y=-2X^2

Y=-2X^2

Y-2X^2

Y=-1X^2,Y=-2X^2

• Upside down U-shape
• Y-values are negative making the graph flipped

EXPERIMENT 3

Y=2X ^3

Y=2X^3

Y=2X^3

Y=3X^3

Y=2X^3

Y=3X^3

Y=5X^3

Y=5X^3

Y=5X^3

Y=(1/2)X^3

Y=2X^3,Y=3X^3,Y=5X^3

• S-liked shape (closer
• Closer to y-axis

Y=(1/2)X^3

Y=(1/2)X^3

Y=(1/2)X^3

• S-shape is wider
• Further away from y-axis

Y=-1X^3

Y=-1X^3

Y=-1X^3

-2X^3

Y=-2X^3

Y=-2X^3

Y=-1X^3,Y=-2X^3

• S-like shape
• Moves to Q1,Q4
• More narrow
• Closer to y-axis

Y=X^3

Y=X^3

Y=X^3

Y=X^5

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X=X^7

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Y=X^3,Y=X^5,Y=X^7

• Higher odd exponent
• S-like shape
• From x=-1 and X=-1 the s-shape is flatter
• The rest of curve is steep

Y=X^4

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Y=X^6

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Y=X^8

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Y=X^4,Y=X^6,Y=X^8

• Higher even exponent
• U-shape
• From x=-1 and x=1 u-shape is flatter
• The rest of the curve gets steeper