Math 109-50 FA01 -- Precalculus
Study Guide - Exam # 3

1. Given two functions, f and g, find f(g(x))  (Section 4.1 problems 1-12)
2. Given a composite function h, decompose it into two functions, f and g, such that h = f(g(x)) (Section 4.1 problems 13-24)
3. Determine, graphically and algebraically, whether a function is one-to-one; if it is, find a formula for its inverse (Section 4.1 problems 48-52, 65-80)
4. Graph a function of the form ab^x+c + d  by first describing how it can be obtained from b^x, locating the horizontal asymptote and where (0,1) has moved to, and then graphing it.  (Section 4.2 problems 19-34)
5. Find, by hand, logarithms of numbers which are related easily to the base. (Section 4.3 problems 5-16)
6. Graph a function of the form blog_a(x + c) + d  by first describing how it can be obtained from log_ax, locating the vertical asymptote and where (1,0) has moved to, and then graphing it.  (Section 4.3 problems 57-64) (includes lnx also)
7. Given a graph of an exponential or logarithmic function of the form b^x+c + d  or log_a(x + c) + d , determine which it is and find c and d.  (none exactly like this, but Section 4.2 problems 45-58 includes these for exponential functions; also, review exercises p. 357 problems 12-17)
8. Given an expression with logarithms, either expand in terms of sums and differences, or express as a single logarithm. (Section 4.4 problems 17-38)
9. Simplify an expression involving exponential functions and logarithms.  (Section 4.4 problems 49-58)
10. Solve equations involving exponential functions or logarithms.  Given an expression with logarithms, either expand in terms of sums and differences, or express as a single logarithm. (Section 4.4 problems 17-38)
11. Simplify an expression involving exponential functions and logarithms.  (Section 4.5 problems 7-20, 33-40)
12.  Given that a phenomenon is growing or decaying exponentially, and given the value of the phenomenon at two times, find the general formula for its growth or decay and the value at another time, by finding the constants P₀ and k in  P = P₀e^kt. (Section 4.6 problems 12-14)