Question

The graph of the parent function is horizontally stretched by a factor of 2, reflected over the y-axis, and then translated 3 units up. What is the equation of the transformed function?

Answer 1

To transform the parent function by a horizontal stretch by a factor of 2, a reflection over the y-axis, and a translation 3 units up, the transformed function would be g(x) = f(-1/2x) + 3. For example, a parent function y = mx + b would become y = -2mx + 3 after these transformations.

Step-by-step explanation:

The transformation of a parent function can be described using the various operations applied to it, such as horizontal stretches, reflections, and translations.

In this case, we have three transformations to apply:

1. A horizontal stretch by a factor of 2 can be represented by multiplying the x-value by 1/2 (because it takes a wider range for x to cover the same amount of change in the function's values).
2. A reflection over the y-axis changes the sign of x (making it negative if it was positive and vice versa).
3. A translation 3 units up adds 3 to the function's value.

If we consider the parent function to be f(x), the transformed function after these operations would be: g(x) = f(-1/2x) + 3

For example, if the parent function was a simple linear function y = mx + b, then after these transformations, the new equation would take the form y = -2mx + 3, assuming the factor of 2 applies to the slope and remembering to include the vertical translation.