1. What similarities exists between function translations?[br]2. How does f(x) change based on a, h, and k?
Linear Function (Point Slope Form)[br][math]f\left(x\right)=a\left(x+h\right)+k[/math][br][br]Use the green, red, and blue buttons to observe the effect of a, h, and k[br]Answer the following questions[br]1. How does a affect the graph?[br]2. How does h affect the graph?[br]3. How does k affect the graph?
Quadratic Function (Vertex Form)[br][math]f\left(x\right)=a\left(x+h\right)^2+k[/math][br][br]Use the green, red, and blue buttons to observe the effect of a, h, and k[br]Answer the following questions[br]1. How does a affect the graph?[br]2. How does h affect the graph?[br]3. How does k affect the graph?
Radical Function[br][math]f\left(x\right)=a\sqrt{x+h}+k[/math][br][br]Use the green, red, and blue buttons to observe the effect of a, h, and k[br]Answer the following questions[br]1. How does a affect the graph?[br]2. How does h affect the graph?[br]3. How does k affect the graph?
Hyperbolic Function[br][math]f\left(x\right)=a\frac{1}{x+h}+k[/math][br][br]Use the green, red, and blue buttons to observe the effect of a, h, and k[br]Answer the following questions[br]1. How does a affect the graph?[br]2. How does h affect the graph?[br]3. How does k affect the graph?
Given any function f(x), how might you expect f(x-3) to behave?
Given any function f(x), how might you expect f(x)+5 to behave?
Given any function f(x), how might you expect -3f(x) to behave?