Part 5: Horizontal Stretches and Compressions Use a graphing utility to display the graphs of the transformations of the function. Use the results to describe the effect has on the graph of describe the transformation resulting from. k f; Example: Use the graph of the function to answer the following. Given the point (-2, 6) is on the graph of . What point is on the graph of ? is (circle one) Mathematical Models; Building Functions (2.6) Learning Objectives: 1. Build and Analyze Functions Examples: A rectangle is inscribed in a circle of radius 3 centered at the origin. Let be a point in quadrant I that is a vertex of the rectangle and is on the circle. Express the area of the rectangle as a function A of and the perimeter of the rectangle as a function of Find the maximum area. For what value x P x. of is the area the largest? For what value of is the perimeter the largest? 2. Let be a point on the graph of . Express the distance from to the d P point (2, 0) as function of What is if ? For what values of is the distance the smallest? x. d 3. A right triangle has one vertex on the graph of , , at , another at the origin, and the third on the positive at . Express the area of the x-axis A triangle as a function of x. 4. An open box with a square base is to be made from a square piece of cardboard 18 inches on a side by cutting out a square from each corner and turning up the sides. Express the volume of the box V
Part 5: Horizontal Stretches and Compressions Use a graphing utility to display the graphs of the transformations of the function. Use the results to describe the effect k has on the graph of f; describe the transformation resulting from. Example: Use the graph of the function to answer the following. Given the point (-2, 6) is on the graph of . What point is on the graph of ? is (circle one) Mathematical Models; Building Functions (2.6) Learning Objectives: 1. Build and Analyze Functions Examples: A rectangle is inscribed in a circle of radius 3 centered at the origin. Let be a point in quadrant I that is a vertex of the rectangle and is on the circle. Express the area A of the rectangle as a function of x and the perimeter P of the rectangle as a function of x. Find the maximum area. For what value of is the area the largest? For what value of is the perimeter the largest? 2. Let be a point on the graph of . Express the distance d from P to the point (2, 0) as function of x. What is d if ? For what values of is the distance the smallest? 3. A right triangle has one vertex on the graph of , , at , another at the origin, and the third on the positive x-axis at . Express the area A of the triangle as a function of x. 4. An open box with a square base is to be made from a square piece of cardboard 18 inches on a side by cutting out a square from each corner and turning up the sides. Express the volume V of the box