The domain of a function may be restricted algebraically, graphically, or For any in the domain of determine (f) x f, f(x). by the practical situation modeled by a function. Represent relations and functions using verbal descriptions, tables, Discontinuous domains and ranges include those with removable (holes) equations, and graphs. Given one representation, represent the relation and nonremovable (asymptotes) discontinuities. in another form. (g) A function can be described on an interval as increasing, decreasing, or Describe the end behavior of a function. (h) constant over a specified interval or over the entire domain of the Determine the equations of vertical and horizontal asymptotes of function. functions (rational, exponential, and logarithmic). (i) A function, is increasing over an interval if the values of f(x), f(x) Determine the inverse of a function (linear, quadratic, cubic, square consistently increase over the interval as the values increase. x root, and cube root). (j) A function, is decreasing over an interval if the values of f(x), f(x) Graph the inverse of a function as a reflection over the line = (j) y x. consistently decrease over the interval as the values increase. x Determine the composition of two functions algebraically and A function, is constant over an interval if the values of remain f(x), f(x) graphically. (k) constant over the interval as the values increase. x Investigate and analyze characteristics and multiple representations of functions with a graphing utility. (a, b, c, d, e, f, g, h, i, j, k)
The domain of a function may be restricted algebraically, graphically, or by the practical situation modeled by a function. Discontinuous domains and ranges include those with removable (holes) and nonremovable (asymptotes) discontinuities. A function can be described on an interval as increasing, decreasing, or constant over a specified interval or over the entire domain of the function. A function, f(x), is increasing over an interval if the values of f(x) consistently increase over the interval as the x values increase. A function, f(x), is decreasing over an interval if the values of f(x) consistently decrease over the interval as the x values increase. A function, f(x), is constant over an interval if the values of f(x) remain constant over the interval as the x values increase. For any x in the domain of f, determine f(x). (f) Represent relations and functions using verbal descriptions, tables, equations, and graphs. Given one representation, represent the relation in another form. (g) Describe the end behavior of a function. (h) Determine the equations of vertical and horizontal asymptotes of functions (rational, exponential, and logarithmic). (i) Determine the inverse of a function (linear, quadratic, cubic, square root, and cube root). (j) Graph the inverse of a function as a reflection over the line y = x. (j) Determine the composition of two functions algebraically and graphically. (k) Investigate and analyze characteristics and multiple representations of functions with a graphing utility. (a, b, c, d, e, f, g, h, i, j, k)
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