Question

Describe how the graph of y = -2f[3(x-4)]-5 can be obtained from the graph of f(x)=x^4. Be sure to use full sentences when describing the transformations.

a) The graph is shifted left by 4 units, vertically compressed by a factor of 3, reflected vertically, and shifted downward by 5 units.
b) The graph is shifted right by 4 units, vertically expanded by a factor of 3, reflected horizontally, and shifted upward by 5 units.
c) The graph is shifted left by 3 units, vertically compressed by a factor of 4, reflected horizontally, and shifted downward by 2 units.
d) The graph is shifted right by 3 units, vertically expanded by a factor of 4, reflected vertically, and shifted upward by 2 units.

Answer 1

The graph of y = -2f[3(x-4)]-5 can be obtained from the graph of f(x)=x^4 by applying a series of transformations: left shift by 4 units, vertical compression by a factor of 3, vertical reflection, and downward shift by 5 units.

Step-by-step explanation:

The graph of the function y = -2f[3(x-4)]-5 can be obtained from the graph of f(x)=x^4 by applying a series of transformations.

First, the graph is shifted left by 4 units. This means that every x-coordinate of the original graph is decreased by 4.

Next, the graph is vertically compressed by a factor of 3. This means that the y-coordinates of the original graph are multiplied by 3.

Then, the graph is reflected vertically. This means that the sign of the y-coordinates is negated.

Finally, the graph is shifted downward by 5 units. This means that every y-coordinate of the transformed graph is decreased by 5.