Question

Describe the transformations from the parent function? a) Multiplying the function by a constant

b) Adding a constant to the function
c) Reflecting the function across the x-axis
d) Reflecting the function across the y-axis

Answer 1

The transformations of a parent function include vertical stretching/compression by multiplying with a constant, vertical translation by adding a constant, and reflections across the x-axis and y-axis which flip the function vertically or horizontally.

Step-by-step explanation:

When we describe the transformations of a parent function, we're looking at how to modify its graph. Here are the transformations associated with different operations:

• Multiplying the function by a constant other than zero will stretch or compress it vertically. If the constant is greater than 1, the function stretches upward, effectively increasing the distance between points on the graph and the x-axis. If the constant is between 0 and 1, the function compresses downward, bringing points closer to the x-axis.
• Adding a constant to the function will translate it vertically. If the constant is positive, every point on the graph will move up by that amount, and if the constant is negative, every point will move down.
• A reflection across the x-axis will invert the function vertically, flipping it upside down. This is equivalent to multiplying the entire function by -1.
• A reflection across the y-axis will invert the function horizontally, creating a mirror image across the y-axis. This can be achieved by replacing every x with -x in the function.