F(s - a) "Y(s) – s"-ly(0) -...- y(n-1)(0) L{f *g} F(8) G(s) -as L{U (t – a)} L{f(t - a)U (t – a)} e-as F(s) MISCELLANEOUS FORMULAS yıf W' %3D W Yn ... /2 .... W (n) ...

1 Find the extrema of the function f(x)= 2-e-* a) (2, e-?) b) no relative extrema c) (2, e²), (0, 0) d) (0, 1) e) (1, 2), (2, e-?)

= M is the transformation of the graph of y = -'/x shifted (2) The graph of f(x) (A) 2-units left and 3-units up (C) 2-units left and 1-unit up (B) 2-units right and 3-units up (D) 2-units right and 1-unit up

6. AVERAGE RATE OF CH ANGE The average rate of change of the function y = f(x) between x = a and x = change in y f(b) – f(a) b – a average rate of change change in x The average rate of change is the slope of the secant line between x = a and x = 1 on the graph of f, that is, the line that passes through (a, f(a)) and (b, f(b)). f(b) – f(a) b- a yA average rate of change f(b)- y = f(x) f(b) - f(a) fla)t 0. a Using the information above, find the average rate of change of the following functions in the given interval: a) **Let f(x)= 3x – 5. Find the average rate of change of f(x) on the interval [0, 1]. Then find it on the interval [3, 7]. Please explain your answer. You can use the graph for the explanation. b) Let f(x)=(x – 3)². Find the average rate of change of f(x) on the interval [1, 3]. Then find it on the interval [4, 7]. Please explain your answer. You can use the graph for the explanation.

The percentage of female high school graduates who enrolled in college is given in the table below. Year 1970 1980 1990 2000 2010 College Enrollment Percentages for Females 25.5 30.3 38.3 45.6 50.5 Let a represent time (in years) since 1970, and let y represent the corresponding percentage of female high school graduates who enrolled in college. Find the cubic regression model y = F(x) = ax³ + bx² + cx + d, = where a is rounded to 6 decimal places, b is rounded to 4 decimal places, c is rounded to 3 decimal places, and d is rounded to 1 decimal place.