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?
Study Notes
Graph Transformations
-
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.
-
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore the key concepts of graph transformations in Algebra 2 with this set of flashcards. Learn how to shift graphs vertically and horizontally by modifying the function's formula. Perfect for students looking to master these essential skills in graphing functions.
