Unit 3 Functions and Graphs PreCalculus 3-R

Evaluate the function f (x) = x2 + 6x at f (8). Evaluate the function at f (6). f (6) = 28 Review Problems 1

Review Problems 2 f (1) = 1, f (3) = 18, f (7) = 50 Evaluate the following piecewise defined function at f (1), f (3), and f (7). f (1) = 1, f (3) = 18, f (7) = 50 Determine whether the equation defines y as a function of x Yes Review Problems 2

Use the function f (x) = x2 + 1 to evaluate the following expressions and simplify. f (x + 5) and f (x) + f (5) For the function , find . Review Problems 3

Review Problems 4 What is the domain of the function

Sketch the graph of the piecewise defined function Review Problems 5

Sketch the graph of the piecewise defined function Review Problems 6

Sketch the graph of the piecewise defined function Review Problems 7

Determine whether the equation defines y as a function of x. Consider a family of functions. How does the value of c affect the graph? The graphs are obtained by shifting the graph of upward c units, Review Problems 8

The graph of g is given. Sketch the graph of the function Review Problems 9

Review Problems 10 f (x) = x 2 The function f (x) is reflected in the x-axis and then shifted up 5 units and the graph of g (x) = 5 – x 2 is obtained. What is f (x)? f (x) = x 2 Review Problems 10

The graph of f is given. Sketch the graph of the function y = –f(x) + 3. Review Problems 11

Review Problems 12 Express the function in the form Find the inverse function of Review Problems 12

Use the given graphs of f and g to evaluate g (f (5)). 3 Review Problems 13

For find Find the inverse function of Review Problems 14

Review Problems 15 A function f is given.  Sketch the graph of f. Use the graph of f to sketch the graph of . Find Review Problems 15

Review Problems 16 –5 f –1(x) = x – 8 Assume f is a one-to-one function. If f (x) = 3 – 6x, find f –1 (33). –5 Use the Property of Inverse Functions to find the inverse function of f(x) = x + 8 f –1(x) = x – 8 Review Problems 16

Review Problems 17 Find the inverse function of

Review Problems 18 Express the function in the form -2 evaluate f(g(–1)). -2 Review Problems 18

Use the given graphs of f and g to evaluate g (f (5)) 3 Review Problems 19

Review Problems 20 Find the domain of Suppose that g(x) = 5x + 3 and h(x) = 25x2 + 30x + 19. Find a function f, such that f(g(x)) = h(x). f(x) = x 2 + 10 Review Problems 20

Review Problems 21 A function f is given Sketch the graph of f. Use the graph of f to sketch the graph of . Find Review Problems 21

Review Problems 22 A one-to-one function is given Find the inverse of the function. Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line y=x. Review Problems 22

Review Problems 23 A one-to-one function is given Find the inverse of the function. Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line y=x. Review Problems 23

Assume f is a one-to-one function. If f (x) = 3 – 6x, find f –1 (33). -5 Use the Property of Inverse Functions to find the inverse function of f(x) = x + 8. f –1(x) = x – 8 Review Problems 24

Review Problems 25 Find the inverse function of

Review Problems 26 x + y – 2 = 0 3x – y – 2 = 0 Find an equation of the line that satisfies the given conditions Through (-2, 4); slope – 1 y-intercept = - 2; slope 3 x + y – 2 = 0 3x – y – 2 = 0 Review Problems 26

Find an equation of the line that satisfies the given conditions Through (4, 5); parallel to the x-axis Through (4, 5); parallel to the y-axis y = 5 x = 4 Review Problems 27

Review Problems 28 5x – 2y + 1 = 0 x – y + 6 = 0 Find an equation of the line that satisfies the given conditions Through (–1, –2); perpendicular to the line 2x + 5y + 8 = 0 Through (1, 7); parallel to the line passing through (2, 5) and (– 2, 1) 5x – 2y + 1 = 0 x – y + 6 = 0 Review Problems 28

A taxi company charges $3 A taxi company charges $3.00 for the first mile (or part of a mile) and 30 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a function of the distance x traveled (in miles) for 0 < x < 2 Review Problems 29

Answers 3 Yes f (x) = x 2 No f (6) = 28 f (8) = 112 f (1) = 1, The graphs are obtained by shifting the graph of upward c units, f (8) = 112 f (6) = 28 f (1) = 1, f (3) = 18, f (7) = 50 Yes f (x) = x 2 3 Answers

Answers 3 f(x) = x 2 + 10 –5 f –1(x) = x – 8 -5 -2 f –1(x) = x – 8 x + y – 2 = 0 3x – y – 2 = 0 f(x) = x 2 + 10 y = 5 x = 4 5x – 2y + 1 = 0 x – y + 6 = 0 Answers