Starting with the function [math]x[/math], is it possible to build any possible linear function of the form [math]mx + b[/math] using these transformations? [i][b]If yes, can you prove it? If no, can you find a counterexample?[/b][/i][br][br]Starting with the function [math]x^2[/math], is it possible to build any possible quadratic function of the form [math]ax^2 + bx + c[/math] using these transformations? [i][b]If yes, can you prove it? If no, can you find a counterexample?[/b][/i][br][br]Starting with the function [math]|x|[/math], is it possible to build any possible absolute value function of the form[br] [math]a|x – b| + c[/math] using these transformations? [i][b]If yes, can you prove it? If no, can you find a counterexample?[/b][/i][br][br][i][b]Can you build a constant function with this environment? Why or why not?[/b][/i][br][br]Think about the following questions. For the cases examined in this environment[br][br]• Vertical sliding of f(x) leads to f(x) + a. [Which way does the function slide if a > 0? a < 0?][br][br]• Horizontal sliding of f(x) leads to f(x+a). [Which way does the function slide if a > 0? a < 0?][br][br]• Vertical stretching & squeezing of f(x) leads to af(x). [What happens to the function if a < 0? 0 < a < 1? a > 1? ][br][br]• Horizontal stretching & squeezing of f(x) leads to af(x). [What happens to the function if a < 0? 0< a < 1? a > 1? ][br]Do you believe these statements are true for any function of one variable? If so, can you prove it? If not, can you find a counterexample?[br][br]Can you build a cubic function with this environment? Why or why not?