TEKS: Chapter 111. Mathematics See All Teacher Resources

111.48.c.3

(3) Patterns and structure. The student applies mathematical processes to understand the connections among representations of functions and combinations of functions, including the constant function, f(x) = x, f(x) = x2, f(x) = √x, f(x) = 1/x, f(x) = x3, f(x) = 3√x, f(x) = bx, f(x) = |x|, and f(x) = logb (x) where b is 10 or e; functions and their inverses; and key attributes of these functions. The student is expected to:

• (A) compare and contrast the key attributes, including domain, range, maxima, minima, and intercepts, of a set of functions such as a set comprised of a linear, a quadratic, and an exponential function or a set comprised of an absolute value, a quadratic, and a square root function tabularly, graphically, and symbolically;

• (B) compare and contrast the key attributes of a function and its inverse when it exists, including domain, range, maxima, minima, and intercepts, tabularly, graphically, and symbolically;

• (C) verify that two functions are inverses of each other tabularly and graphically such as situations involving compound interest and interest rate, velocity and braking distance, and Fahrenheit-Celsius conversions;

• (D) represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations such as combining a 20% discount and a 6% sales tax on a sale to determine h(x), the total sale, f(x) = 0.8x, g(x) = 0.06(0.8x), and h(x) = f(x) + g(x);

• (E) model a situation using function notation when the output of one function is the input of a second function such as determining a function h(x) = g(f(x)) = 1.06(0.8x) for the final purchase price, h(x) of an item with price x dollars representing a 20% discount, f(x) = 0.8x followed by a 6% sales tax, g(x) = 1.06x; and

• (F) compare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically such as a quadratic function that results from multiplying two linear functions.