The parent function is the simplest form of the type of function given.

Remove parentheses.

Remove parentheses.

Multiply .

Combine and .

Rewrite as .

Multiply the exponents in .

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.

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