# IM1.5.9 Explore function transformations 1: Range

- Author:
- Lind, Jon

- Topic:
- Functions

## Adding to the Range

Today, we're going to explore how to change the graph of a function by adding to the function's equation.
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*and*g*, graph the points on the coordinate plane by selecting both columns (*x*and*f(x)*) and creating a list of points1. Look at the individual points you graphed above. How do the outputs from g differ from the outputs from f? 2. What appears to be the effect of subtracting 3 from a function? 3. Make a conjecture: what would happen if you graphed a new function ? Test your conjecture by graphing h(x) above (type |x|+2 in an empty cell) 4. Generalize: How does the graph of f(x) compare to the graph of f(x)+k? (use your vocabulary from geometry!)

## Multiplying the Range

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. Look at the individual points you graphed above. How do the outputs from a and b differ from the outputs from f? 2. What appears to be the effect of multiplying the outputs of a function? 3. Generalize: How does the graph of f(x) compare to the graph of k·f(x)? (might need some new vocabulary for this one)