Describe the Transformation y=-2/3(4)^(x+3)-4

Math
The parent function is the simplest form of the type of function given.
Solve for .
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Remove parentheses.
Remove parentheses.
Simplify .
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Multiply .
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Combine and .
Rewrite as .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Apply the distributive property.
Multiply by .
Use the power rule to combine exponents.
Add and .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
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Rewrite as .
Move the negative in front of the fraction.
For a better explanation, assume that is and is .
The transformation from the first equation to the second one can be found by finding , , and for each equation.
Find , , and for .
Find , , and for .
The horizontal shift depends on the value of . The horizontal shift is described as:
– The graph is shifted to the left units.
– The graph is shifted to the right units.
Horizontal Shift: Left Units
The vertical shift depends on the value of . The vertical shift is described as:
– The graph is shifted up units.
– The graph is shifted down units.
Vertical Shift: None
The sign of describes the reflection across the x-axis. means the graph is reflected across the x-axis.
Reflection about the x-axis: Reflected
The value of describes the vertical stretch or compression of the graph.
is a vertical stretch (makes it narrower)
is a vertical compression (makes it wider)
Vertical Compression: Compressed
To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.
Parent Function:
Horizontal Shift: Left Units
Vertical Shift: None
Reflection about the x-axis: Reflected
Vertical Compression: Compressed
Describe the Transformation y=-2/3(4)^(x+3)-4

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