TEKS: Chapter 111. Mathematics See All Teacher Resources

111.40.c.5

(5) Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:

• (A) determine the effects on the key attributes on the graphs of f(x) = b^x and f(x) = log_b (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d;

• (B) formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;

• (C) rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations;

• (D) solve exponential equations of the form y = ab^x where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions; and

• (E) determine the reasonableness of a solution to a logarithmic equation.