FNGR 1 | Lesson 4 | Explore (Vertical Translations)

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 $$f(x)-k$$.

Example:

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:

x $$f(x)=2^x$$
-2 $$\large \frac{1}{4}$$
-1 $$\large \frac{1}{2}$$
0 1
1 2
2 4
x $$f(x)=2^x+3$$
-2 $$3 \Large \frac{1}{4}$$
-1 $$3 \Large \frac{1}{2}$$
0 4
1 5
2 7

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?