A vertical transformation occurs when we add or subtract a constant value from the outputs, or the function itself. It is represented as either \(f(x)+k\) or \(f(x)-k\).
The parent function for the exponential is \(f(x)=2^x\):
If we translate this graph up 3 units we end up with this graph:
The new equation for the function is \(f(x)=2^x+3\).
Examine the table of values for the original and the new functions:
What do you notice? What do you wonder? Describe what you think is happening in your own words. How does this compare to the graphs above?