Unit 3 Functions and Graphs Pre Calculus 3

Unit 3 Functions and Graphs Pre. Calculus 3 -R

• Evaluate the function f (x) = x 2 + 6 x at f (8) = 112 • Evaluate the function at f (6) = 28 1 Review Problems

• 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 2 Review Problems

• Use the function f (x) = x 2 + 1 to evaluate the following expressions and simplify. f (x + 5) and f (x) + f (5) • For the function 3 , find. Review Problems

• What is the domain of the function �What is the domain of the function 4 Review Problems

• Sketch the graph of the piecewise defined function 5 Review Problems

• Sketch the graph of the piecewise defined function 6 Review Problems

• Sketch the graph of the piecewise defined function 7 Review Problems

• Determine whether the equation defines y as a function of x. No • 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, 8 Review Problems

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

• 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 10 Review Problems

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

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

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

• For find • Find the inverse function of 14 Review Problems

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

• Assume f is a one-to-one function. • If f (x) = 3 – 6 x, 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 16 Review Problems

• Find the inverse function of 17 Review Problems

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

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

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

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

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. 22 Review Problems

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. 23 Review Problems

Assume f is a one-to-one function. If f (x) = 3 – 6 x, 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 24 Review Problems

Find the inverse function of 25 Review Problems

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

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

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

• 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 29 Review Problems

1. 2. 3. 4. 5. 6. 7. f (8) = 112 f (1) = 1, f (3) = 18, f (7) = 50 f (6) = 28 Yes 8. 9. No The graphs are obtained by shifting the graph of upward c units, 10. 11. 12. 13. 3 14. 15. Answers f (x) = x 2

16. 17. – 5 18. 19. 3 20. 21. f – 1(x) = x – 8 23. -2 f(x) = x + 10 24. 25. 26. -5 x+y– 2=0 3 x – y – 2 = 0 2 27. 28. y=5 x=4 5 x – 2 y + 1 = 0 x–y+6=0 22. 29. Answers f – 1(x) = x – 8