Question

What transformation(s) of the parent graph of f(x) = x produces the graph of

k(x) = 14x + 12 - 1?

Answer 1

The graph of k(x) = 14x + 11 is produced by applying a vertical stretch by a factor of 14 and a vertical shift up by 11 units to the parent function f(x) = x.

Step-by-step explanation:

The student is asking about the transformations that turn the parent function f(x) = x into k(x) = 14x + 11. To achieve this transformation, we perform two operations on f(x):

1. Vertical Stretch by a factor of 14, which multiplies each y-value by 14, drastically changing the slope of the line.
2. Vertical Shift by 11 units upwards, which adds 11 to each y-value of f(x), moving the entire graph up.

These operations convert the parent function into the given function k(x). Recognizing how algebraic manipulation affects the graphical representation is important for understanding function transformations.