Name ______________________
Trial # 1:
What Makes a Function Linear or Nonlinear?
y=2x+1
Trial # 2:
y=2x2+1
1.
Make a prediction about whether the equation
y=2x +1 is a linear function or a nonlinear
function .
1.
Make a prediction about whether the equation
y=2x2 +1 is a linear function or a nonlinear
function .
2.
Input the equation into a graphing calculator.
2.
Input the equation into a graphing calculator.
3.
Sketch the graph.
3.
Sketch the graph.
4.
Is the function linear or nonlinear? How do you
know?
4.
Is the function linear or nonlinear? How do you
know?
What Makes a Function Linear or Nonlinear?
Trial # 3:
y=-x+1
Trial # 4:
y=2x3+1
1.
Make a prediction about whether the equation
y=-x+1 is a linear function or a nonlinear function.
1.
Make a prediction about whether the equation
y=2x3 + 1 is a linear function or a nonlinear
function .
2.
Input the equation into a graphing calculator.
2.
Input the equation into a graphing calculator.
3.
Sketch the graph.
3.
Sketch the graph.
4.
Is the function linear or nonlinear? How do you
know?
4.
Is the function linear or nonlinear? How do you
know?
What Makes a Function Linear or Nonlinear?
Trial # 5:
y=4x-1
Trial # 6:
y=4x-1
1.
Make a prediction about whether the equation
y=4x-1 is a linear function or a nonlinear function
.
1.
Make a prediction about whether the equation
y=4x-1 is a linear function or a nonlinear function .
2.
Input the equation into a graphing calculator.
2.
Input the equation into a graphing calculator.
3.
Sketch the graph.
3.
Sketch the graph.
4.
Is the function linear or nonlinear? How do you
know?
4.
Is the function linear or nonlinear? How do you
know?
What Makes a Function Linear or Nonlinear?
Trial # 7:
y=5/x
Trial # 8:
y=3x + 22
1.
Make a prediction about whether the equation
y=5/x is a linear function or a nonlinear function .
1.
Make a prediction about whether the equation
y=3x + 22 is a linear function or a nonlinear
function .
2.
Input the equation into a graphing calculator.
2.
Input the equation into a graphing calculator.
3.
Sketch the graph.
3.
Sketch the graph.
4.
Is the function linear or nonlinear? How do you
know?
4.
Is the function linear or nonlinear? How do you
know?
Conclusions:
Based on your trials, what conclusions can you draw about linear functions?
1.
A linear function will have an equation that______________________________________.
2.
A linear function will have an equation that doesn’t _______________________________.
Based on your trials, what conclusions can you draw about nonlinear functions?
1.
A nonlinear function will have an equation that___________________________________.
2.
A nonlinear function will have an equation that doesn’t ____________________________.
What questions do you still have about what makes functions linear or nonlinear?
1.
One question I still have is ____________________________________________________
_____________________________________________________________________________
2. Another question I have is _____________________________________________________
_____________________________________________________________________________