functions graphically Now, on to more practice with Section 1.3b: Today, we analyze functions graphically and explore piecewise functions…

Quality Practice Problems Graph the given function, then answer the following questions: 8 1. On what intervals is the function increasing or decreasing? Inc: [ 2, ) Dec: (– , 2 ] 8 2. Is the func. even, odd, or neither? Neither 3. What are the extrema of the func.? Min. of 0 at x = 2 4. Does the graph relate to one of the 12 basic functions? If so, how? The squaring func., shifted right 2 5. What is the domain and range of the function? D: (– , ) 8 8 R: [ 0, ) 8

Quality Practice Problems Graph the given function, then answer the following questions: 1. On what intervals is the function increasing or decreasing? 8 Dec: [ – 4, ) 2. Is the func. even, odd, or neither? Neither 3. What are the extrema of the func.? Max. of 0 at x = – 4 The square root func., shifted left 4, reflected across x-axis 4. Does the graph relate to one of the 12 basic functions? If so, how? 5. What is the domain and range of the function? D: [ – 4, ) 8 R: ( – , 0 ] 8

Quality Practice Problems Graph the given function, then answer the following questions: 8 1. On what intervals is the function increasing or decreasing? Inc: ( – , –1 ] Dec: [ –1, ) 8 2. Is the func. even, odd, or neither? Neither 3. What are the extrema of the func.? Max. of 5 at x = –1 The abs. val. function, reflected across x-axis, shifted left 1, up 5 4. Does the graph relate to one of the 12 basic functions? If so, how? 5. What is the domain and range of the function? D: (– , ) 8 8 R: (– , 5 ] 8

So, what are these functions with “smart parts?” Piecewise Functions!!!

x if x > 0 f(x) = –x if x < 0 Which of the twelve basic functions has the following piecewise definition over separate intervals of its domain? x if x > 0 f(x) = –x if x < 0 This is the absolute value function!!!

8 8 8 Function is continuous! D: (– , ) R: [0, ) Sketch the given function (without using your calculator!), list any points of discontinuity, and state the domain and range of the function. Function is continuous! D: (– , ) 8 8 R: [0, ) 8

Point of discontinuity Sketch the given function (without using your calculator!), list any points of discontinuity, and state the domain and range of the function. Point of discontinuity at x = 0 D: (– , ) 8 8 R: (– , 0 ] U ( 1, ) 8 8

Point of discontinuity Sketch the given function (without using your calculator!), list any points of discontinuity, and state the domain and range of the function. Point of discontinuity at x = 0 8 8 D: (– , ) R: (– , ) 8 8

8 8 8 Function is continuous! D: (– , ) R: [ 0, ) Sketch the given function (without using your calculator!), list any points of discontinuity, and state the domain and range of the function. Function is continuous! D: (– , ) 8 8 R: [ 0, ) 8

Point of discontinuity Sketch the given function (without using your calculator!), list any points of discontinuity, and state the domain and range of the function. Point of discontinuity at x = 2, 3, 4, 5,… 8 8 D: (– , ) R: [ 0, ) 8

Whiteboard Problems Graph the given function, then answer the following questions: 1. On what intervals is the function increasing or decreasing? Inc: [ 0, ) 8 Dec: (– , 0 ] 8 2. Is the func. even, odd, or neither? Even 3. What are the extrema of the func.? Min. of 3 at x = 0 4. Does the graph relate to one of the 12 basic functions? If so, how? The abs. val. function, shifted up 3 5. What is the domain and range of the function? D: (– , ) 8 8 R: [ 3, ) 8

Whiteboard Problems Graph the given function, then answer the following questions: 1. On what intervals is the function increasing or decreasing? Inc: (– , ) 8 8 2. Is the func. even, odd, or neither? Neither 3. What are the extrema of the func.? No extrema 4. Does the graph relate to one of the 12 basic functions? If so, how? The exp. function, shifted up 2 5. What is the domain and range of the function? D: (– , ) 8 8 R: ( 2, ) 8