Podcast
Questions and Answers
What does the equation $y=f(x)+c$ represent?
What does the equation $y=f(x)+c$ represent?
- The graph shifts up c units (correct)
- The graph shifts left c units
- The graph shifts right c units
- The graph shifts down c units
What happens when you use the equation $y=f(x)-c$?
What happens when you use the equation $y=f(x)-c$?
- The graph shifts down c units (correct)
- The graph shifts left c units
- The graph shifts right c units
- The graph shifts up c units
What effect does the equation $y=f(x+c)$ have on the graph?
What effect does the equation $y=f(x+c)$ have on the graph?
- Shifts right c units
- Shifts down c units
- Shifts left c units (correct)
- Shifts up c units
Which transformation occurs with the equation $y=f(x-c)$?
Which transformation occurs with the equation $y=f(x-c)$?
What does the equation $y=-f(x)$ do to the graph?
What does the equation $y=-f(x)$ do to the graph?
What transformation is caused by the equation $y=f(-1x)$?
What transformation is caused by the equation $y=f(-1x)$?
What happens to the graph when using the equation $y=cf(x)$ where c > 1?
What happens to the graph when using the equation $y=cf(x)$ where c > 1?
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Study Notes
Graph Transformations
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Vertical Shift Up:
- Formula: ( y = f(x) + c )
- Shifts the graph up by ( c ) units when a constant is added at the end of the function.
-
Vertical Shift Down:
- Formula: ( y = f(x) - c )
- Shifts the graph down by ( c ) units when a constant is subtracted from the function.
-
Horizontal Shift Left:
- Formula: ( y = f(x + c) )
- Shifts the graph left by ( c ) units when the constant is grouped with ( x ) in addition.
-
Horizontal Shift Right:
- Formula: ( y = f(x - c) )
- Shifts the graph right by ( c ) units when the constant is subtracted from ( x ).
-
Reflection Across the X-Axis:
- Formula: ( y = -f(x) )
- Flips the entire graph upside down by multiplying the function by -1.
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Reflection Across the Y-Axis:
- Formula: ( y = f(-1x) )
- Flips the graph horizontally by replacing ( x ) with (-1x).
-
Vertical Stretch:
- Formula: ( y = cf(x) ) where ( c > 1 )
- Stretches the graph vertically by a factor of ( c ), making it taller without moving the x-coordinates. The y-coordinates are multiplied by ( c ).
-
Vertical Compression:
- Formula: ( y = cf(x) ) where ( 0 < c < 1 )
- Compresses the graph vertically by a factor of ( c ), making it shorter.
-
X-Axis Unchanged:
- During vertical transformations, the x-axis remains constant; only y-coordinates change based on the transformations applied.
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