Chapter 2.1, Problem 50E

Looking at the graph of f(x), determine the following below. Show your work. Assume ends of the graph continue. 10- |(0, 8) (0.189, 8.096) -5 G (-2, 0) (1.702, 0) 10 (-3.,523, –4.689) a. Location(s) where f "(x) < 0 b. Location(s) where f'(x) has a minimum c. Sign (positive/negative/zero) of f"(x) at Point G d. Sign (positive/negative/zero) of f '(x) at Point F

Introduction 1. Determine whether the function is even, odd, or neither a. f(x) = 5 – 3x b. f(x) = x* – x² – 1 c. f(x) = 2x³ + 3x Domain, Range and Graphing 2. Find the domain, range for f(x) = x² + 4x + 4 and graph 3. Find the domain, range for f(x) = 2x-3 5-4x and graph 4. Find the domain, range for f(x) = V9x2 – 16 and graph 5. Find the domain for f(x) = log2(x + 2) – 3 Transformation of Graph 6. Use graph of f(x) = x³ to sketch the graph of each function a. f(x) = x3 – 1 b. f(x) = (x + 2)³ +1 7. Sketch the graph for f(x) = -5sinx + 3 Composite Function 8. Solve the following set of function (please simplify): x3 + x2 + 2x f(x) = -,g(x) = 2x² + 2, h(x) = v6x +3 %3D x +1 a. (f • g)x b. (g o h)x Piecewise Defined Function 9. Find the domain, range of the set of piecewise defined function and graph h(x) = {2, x 3 10. Find the domain, range of the set of piecewise defined function and graph x< 2 x2 2 4-x, 1 + 2x, f(x) =

Define the term constant function.

The bar graph shows the wage gap between men and women for selected years Wage Gap Between Men and Women from 1980 through 2020. The function G(x) = - 0.01x2 + x+ 55 models the wage gap, as a percent, x years after 1980. The graph of function G is also shown. Use this information to complete parts a and b. 100- 78% 82% 82% 80구 71% 65% 60- ... 40- a. Find and interpret G(10). 20구 01 1980 1990 2000 2010 2020 O A. G(10)= 71, which represents a wage gap of 71% in the year 1990. Year B. G(10) = 64, which represents a wage gap of $64,000 in the year 1990. The Graph of a Function Modeling the Data C. G(10) = 64, which represents a wage gap of 1% in the year 1990. 100+ D. G(10) = 71, which represents a wage gap of $71,000 in the year 1990. 80구 60- G(x}= -0.01x+x + 55 40- 20- 0+ 5 10 15 20 25 30 35 40 Years after 1980 Wage Gap (percent) Wage Gap (percent)

10. Describes all the features of each function below. The explain how each function was graphed from its original function. )* – 1 a) y = b. f(x) = 3 · 2×-1 c. g(x) = (0.75)3*+2 + 4

Exercises 79-84: Find the domain of the function. Write your answer in interval notation. 79. f(x) = 80. f(x) = s0. f0) x² - 1 6. 81. f(x) = 82. f(x) =: 4x - 1 84. f(x) = x? + 1 + 1 83. f(x) = x + 3

Refer to the graph of the function f in the following figure. = 65 5 -2* (a) Find f(0). f(0) 4 3- 2- 1+ X = (i) f(x) = 3 X = (ii) f(x) = 0 X (b) Find the value of x for which f(x) = 3 and f(x) = 0. X 4 X y = f(x) 5 X