Question

Describe the transformation of the parent function in words and write the equation of the transformed function.

A) f(2x)
B) 2•f(x)
C) f(x) -5
D) f(x)+3
E) f(-x)

Answer 1

The transformations f(2x), 2•f(x), f(x) - 5, f(x) + 3, and f(-x) correspond to a horizontal compression, vertical stretching, downward shift, upward shift, and reflection across the y-axis, respectively.

Step-by-step explanation:

Transformations of Parent Functions

The transformations of a parent function f(x) can be described as follows:

• A) f(2x): This transformation represents a horizontal scaling of the parent function. In particular, it compresses the graph of f(x) by a factor of 2 along the x-axis.
• B) 2•f(x): This transformation indicates a vertical stretching. It multiplies all y-values of the parent function by 2, making the graph taller.
• C) f(x) - 5: This transformation represents a vertical translation. It shifts the graph of f(x) downward by 5 units.
• D) f(x) + 3: This transformation also deals with vertical translation. It shifts the graph of f(x) upward by 3 units.
• E) f(-x): This is a reflection transformation. It reflects the graph of f(x) across the y-axis, creating a mirror image.

Each transformation affects the parent function in a different way, altering its graph without changing its basic shape.