Transformations are really important for understanding how exponential functions behave. Exponential functions look like this:

f(x) = a * b^(x - h) + k

Here’s what each part means:

• a: This affects how the graph stretches or gets squished vertically.
• b: This is the base number. If b is more than 1, the function grows. If it's between 0 and 1, the function shrinks.
• h: This moves the graph left or right.
• k: This moves the graph up or down.

Key Transformations

1. Vertical Stretch or Compression:

   • If |a| is greater than 1, the graph stretches.
   • If |a| is less than 1, the graph gets compressed.

2. Horizontal Shifts:

   • A positive h moves the graph to the left.
   • A negative h moves it to the right.

3. Vertical Shifts:

   • A positive k moves the graph upward.
   • A negative k moves it downward.

Symmetry

Exponential functions are different from other types of functions. They do not have symmetry like even or odd functions do. This means they do not look the same on both sides of the y-axis or the origin. Instead, they grow in unique ways depending on the transformations that are applied to them.