Let's begin by looking at monomial functions such that, when written in algebraic form, the coefficient is 1. This includes functions like f ( x ) = x 2 , g ( x ) = x 3 , and h ( x ) = x 4 . Untried Use the given applet to answer the questions that follow. Three functions f ( x ) = x 2 , g ( x ) = x 3 , and h ( x ) = x 4 are all graphed in the applet, and you can show and hide each function by pressing the buttons under the graph. You can also vary the input quantity for each function by dragging the "x" symbol on the horizontal axis. Drag the purple X to vary the value of x . Hide f Show g Show h Evaluate the functions at each of the following inputs either using the graph or formula. f ( 1 ) = f ( 2 ) = g ( 1 ) = g ( 2 ) = h ( 1 ) = h ( 2 ) = Which of the following are true statements about the behavior of these three functions when x 1 ? Select all that apply. For all three functions, the output value is always positive when x 1 . For all three functions, as x increases by equal amounts (for example, when x = 1 ) the changes in the output value become larger and larger. For all three functions, an input value of 1 produces an output value of 1. At least one of the functions has a constant rate of change over part of its domain. For the same input value x > 1 , functions with a larger exponent produce a larger output value. For all three functions, when x increases the function value increases