# IM1.5.9 Explore Transformations 2: Domain

- Author:
- 00JonLind

## Adding to the domain

In the last task, we (hopefully) discovered that adding a constant to the range of a function translates the function vertically.
1. Make a conjecture: What will happen if we add a constant to the domain (input) of a function?
2. Below, fill in the columns for the range of the functions with the given domain. Use the following rules for your functions:
When you've found all of the range values for

*f,**g, and h*, graph the points on the coordinate plane by selecting both columns (*x*and*f(x)*) and creating a list of points1. Think about the **inputs** you used when finding your points. When x was 1, what did you *actually* plug into the functions?
2. What appears to be the effect of subtracting 3 from the input of a function?
3. Generalize: How does the graph of f(x) compare to the graph of f(x+k)? (use your vocabulary from geometry!)

## Multiplying the domain

Below, fill in the columns for the range of the two functions with the given domain. Use the following rules for your functions:
When you've found all of the range values for

*f,**a, and b*, graph the points on the coordinate plane by selecting both columns (*x*and*f(x), for example*) and creating a list of points1. Think about the **inputs** you used when finding your points. When x was 1, what did you *actually* plug into the functions?
2. What appears to be the effect of multiplying the input of a function by 2?
3. Generalize: How does the graph of f(x) compare to the graph of f(kx)?