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 points

1. 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 andf(x), for example) and creating a list of points

1. 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)?