Cosine Graph Transformations

1. Move the "a" slider back and forth. (a) What happens to the graph as "a" grows positively? (b) What happens to the graph as "a" gets close to zero? (c) What happens to the graph as "a" becomes negative? (d) Name this characteristic of the graph as "a" changes. (e) Using the five points displayed on the graph, sketch the following on your paper. Try to sketch them out first, and then check your graph with the one in the applet. (i) f(x) = 2cos(x) (ii) f(x) = -3cos(x) (iii) f(x) = .5cos(x) Move "a" back to 1 2. Move the "b" slider back and forth. (a) What happens to the graph as "b" grows positively? (b) What happens to the graph as "b" gets close to zero? (c) What are two different ways to describe what is happening to the graph as "b" changes? (d) Using the five points displayed on the graph, sketch the following on your paper. Try to sketch them out first, and then check your graph with the one in the applet. (i) f(x) = cos(2x) (ii) f(x) = cos[(1/2)x] (iii) f(x) = cos(4x) Move the "b" slider back to 1. 3. Move the "h" slider back and forth. (a) What happens to the graph as "h" grows positively? (b) What happens to the graph as "h" grows negatively? (c) What would you name this characteristic of the graph as "b" changes? (d) Using the five points displayed on the graph, sketch the following on your paper. Try to sketch them out first, and then check your graph with the one in the applet. (i) f(x) = cos(x - pi) (ii) f(x) = cos (x + pi/2) (iii) f(x) = cos (x - 3pi/2) Move the "h" slider back to 0. 4. Move the "k" slider back and forth. (a) What happens to the graph as "k" grows positively? (b) What happens to the graph as "k" grows negatively? (c) What would you call this characteristic of the graph as "k" changes? (d) Using the five points displayed on the graph, sketch the following on your paper. Try to sketch them out first, and then check your graph with the one in the applet. (i) f(x) = cos(x) + 2 (ii) f(x) = cos(x) - 1/2