Question

Describe how the graph of each function is related to the graph of its parent function.

5. y=-2^x+1

6. y=3^(x-4)

7. y=5^(x+1)-2

Answer 1

5. reflection in y=0, translation 1 up

6. translation 4 right

7. translation 1 left, 2 down

Explanation:

For parent function f(x), the transformation ...

g(x) = a·f(x -h) +k

represents a vertical scaling by a factor of "a", a translation to the right by an amount "h", and a translation upward by an amount "k". When "a" is negative, it represents a reflection across the x-axis.

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5. a=-1, h=0, k=1. Reflection across the x-axis, then translation upward 1 unit.

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6. a=1, h=4, k=0. Translation to the right 4 units.

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7. a=1, h=-1, k=-2. Translation 1 unit left and 2 units down.