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February 12, 2014 Notes 95 Graphing using transformations When graphing ________________ functions by transformations we always use the key points _____________ and _____________. Vertical shifts and Means to shift the whole graph up or down Vertical stretch Means to stretch the graph vertically by multiplying each y value by a Graphing calculator activity Consider the equation Do you think the graph will move left/right or up/down? Do you think the graph will move left or right? From the graph which direction did it move? Now consider the equation Which direction do you think this graph will move? In general, what can we conclude about horizontal shifts? ALWAYS REMEMBER THAT X’s LIE Horizontal shifts adding a number to the exponent means to shift the graph to the left subtracting a number from the exponent means to shift the graph to the right Always do the _____________ of what the sign says. Remember that x’s lie!
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February 12, 2014
Notes 9-‐5 Graphing using transformations
When graphing ________________ functions by transformations we always use the key points _____________ and _____________.
Vertical shifts and
Means to shift the whole graph up or down
Vertical stretch
Means to stretch the graph vertically by multiplying each y value by a
Graphing calculator activity
Consider the equation
Do you think the graph will move left/right or up/down?
Do you think the graph will move left or right?
From the graph which direction did it move?
Now consider the equation
Which direction do you think this graph will move?
In general, what can we conclude about horizontal shifts?
ALWAYS REMEMBER THAT X’s LIE
Horizontal shifts
adding a number to the exponent means to shift the graph to the left
subtracting a number from the exponent means to shift the graph to the right
Always do the _____________ of what the sign says. Remember that x’s lie!
February 12, 2014
Graphing Horizontal shifts
1. Start at (0,0) and move the amount of the horizontal shift
2. Draw new axis lines to create a new center
3. Then graph the key points (0,1) & (1, b) from the new center
4. Remember:
5. Always Zind a new center when graphing shifts
6. X’s always lie – do the opposite of what it says
Graph Graph
Consider the equation
What do you think will happen to the graph?
What actually happened to the graph?
Consider the equation
What do you think will happen to the graph?
What actually happened to the graph?
In general, what can we conclude about negatives in front of our function?
This is called a ___________________ reZlection, which is a reZlection over the ________-‐axis.
February 12, 2014
Vertical ReZlections
a negative in front means to reZlect the graph over the x-‐axis
Graphing Vertical reZlections
1. Start with the key points
2. Multiply the y-‐value of each key point (0,1) & (0, b) by -‐1
3. Graph the new points
Graph Graph
