Grade 11 Math Project Day Research Paper

11 Math Function Transformations Assignment Name: Jocelyn Witteveen

Grade 11 Math Project Day Assignment

Find out what the following manipulations of a, k, d, and c do. Be sure your results are true for all of the functions.

1. What happens when c is greater than zero? Less than zero? When c is manipulated, is it the Domain (x-values) or Range (y-values) being affected compared to the original graph?

When c is greater than zero, the graph moves up on the y-axis. When it’s less than zero, it moves down on the y-axis. C is the y-value at the start, vertex, or asymptote of the graph. The Range is being affected because c changes the y of the graph.

2. What happens when d is greater than zero? Less than zero? When d is manipulated, is it the Domain

When it’s less than zero, it moves left on the x-axis. D is the x-value with the opposite positive/negative sign at the start, vertex, or asymptote of the graph. The Domain is being affected for the radical and rational function because d changes the start of the graph on the x-axis. The Domain stays the same for the quadratic and absolute functions because they continue for infinity in both directions of the x-axis.

3. What happens when a is positive? What happens when a is negative? When a is manipulated, is it the Domain (x-values) or Range (y-values) being affected compared to the original graph? When a is positive, the graph opens up, into positive y-values (if c is at zero). When it’s negative, it opens down, into negative y-values (if c is at zero). A will determine whether the graph will open up or down, depending on if it’s positive or negative. For the rational function, when a is positive, it stays in the top right and bottom left planes (quadrant 1 and 3). When a is negative, it goes to the opposite planes (quadrant 2 and 4). The Range is being affected because a changes whether the graph will open up or