Daily Warm Up Evaluate 3y= 4x-5 where x = -3 Which of the following equations is a linear function 7y-10 = x b) c)

Function Notation Notes 3.3 Goals: Use function notation to evaluate and interpret functions (day 1) Use function notation to solve and graph functions. (day 2) Solve real-life problems using function notation. (day 3)

Function Notation Function Notation renames “y”as f(x) RECALL: All Linear Equations can be written in y = mx+b form Function Notation renames “y”as f(x) where x is the input & f(x) is the ouput

Function Notation So instead of writing y = mx + b Function Notation looks like f(x) = mx + b Use f, g, or h to notate a function: f(x) or g(x) or h(x)

Example 1 Evaluate f(x) = –4x + 7 when x = 2 & x = –2

Example 2 Let f(t) be the outside temperature (°F) t hours after 6 A.M. Explain the meaning of each statement f(0) = 58 f(6) = n f(3) < f(9)

You Try 1. Evaluate the function when x = -4, 0, & 3 a) f(x) = 2x – 5 b) g(x) = –x –1 2. Let g(t) be the outside temperature (°C) t hours after 9 A.M. Explain the meaning of each statement. a) g(4) = 75 b) g(m) = 70 c) g(2) = g(9) d) g(6) > g(0)

end of day 1

Daily Warm Up Evaluate h(x) = 4x-5 where x = 0,1,2,-4,-6. Evaluate f(x) = -x+10 where x= -3, 0, 1, 2,3

Function Notation Notes 3.3 Goals: Use function notation to evaluate and interpret functions (yesterday) Use function notation to solve and graph functions. (today) Solve real-life problems using function notation. (tomorrow)

Example 3 For , find the value of x for which h(x) = –7.

Example 4 Graph f(x) = 2x + 5 table method x f(x) (x, f(x))

You Try Find the value of x. f(x) = 6x + 9; f(x) = 21 ; g(x)= –1 Graph the linear function g(x) = 3x-2

end of day 2

Daily Warm Up 1. Graph h(x) = -3x + 7 table method x f(x) (x, f(x))

Function Notation Notes 3.3 Goals: Use function notation to evaluate and interpret functions (yesterday) Use function notation to solve and graph functions. (today) Solve real-life problems using function notation. (tomorrow)

Example 5 The graph shows the number of miles a helicopter is from its destination after x hours on its first flight. On its second flight, the helicopter travels 50 miles farther and increases its speed by 25 miles per hour. The function f(x)= 350 – 125x represents the second flight, where f(x) is the number of miles the helicopter is from its destination after x hours. Which flight takes less time? Explain.

You Try Let f(x) = 250 – 75x represent the second flight, where f(x) is the number of miles the helicopter is from its destination after x hours. Which flight takes less time? Explain.

end of day 3