Bound Triangle Problems
Change the values of a to select x-values for h(x) = 9-x^2
Consider the triangle with its base on the x-axis with endpoints at (-3,0) and (3,0). The height is deﬁned by , for . 1) What is the height when Sketch the triangle. 2) For which value(s) of x is the height 5? Sketch the triangle(s). 3) What are the possible values for the height of the triangle? 4) How do the values you determined in #3 relate to the domain or range of the function ? 5) For what values of is the height maximized? 6) What are the possible values for the area of the triangle? 7) For what values of x is the area maximized? 8) Write a function g describing the area as a function of the height h. What are the domain and range of g. 9) Write a function A for the area as a function of x. What are the domain and range of A? 10) What is the relationship between A, g, and h?