Question

Describe two transformations of the graph of f(x)=x^5 where the order in which the transformations are performed is important. Then describe two transformations where the order is not important. Explain reasoning

Answer 1

Two transformations of the graph of f(x)=x^5 where the order is important are scaling and translation. Two transformations where the order is not important are reflection and rotation.

Step-by-step explanation:

Two transformations of the graph of f(x) = x^5 where the order is important are scaling and translation.

Scaling: To scale the graph vertically, multiply the function by a constant. For example, if you multiply f(x) by 2, the graph will be stretched vertically.

Translation: To translate the graph horizontally or vertically, add or subtract a constant. For example, if you add 3 to f(x), the graph will be shifted 3 units to the left.

Two transformations where the order is not important are reflection and rotation.

Reflection: To reflect the graph over the x-axis, negate the value of f(x). This will flip the graph upside down.

Rotation: To rotate the graph, replace x with x - a in the function. This will shift the graph a units to the right.