TEKS: Chapter 111. Mathematics See All Teacher Resources

111.40.c.2

(2) Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse. The student is expected to:

• (A) graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b^x, f(x)=|x|, and f(x)=log_b (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval;

• (B) graph and write the inverse of a function using notation such as f ^-1 (x);

• (C) describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and

• (D) use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.