Print this Page
4.4 – Shifting Functions
- Describe how the equation of a graph changes when it is shifted horizontally, vertically, or both.
- Given a function and its graph, write the equation of a function for a graph that has been shifted from the original graph
- Horizontally – To the left or right.
- Shift – To move from one place to another.
- Vertically – Up or down.
- Shifting Functions involves adding positive or negative numbers to parts of parent functions.
- This works for ALL parent functions: linear, quadratic, absolute value, reciprocal, cubic (), quartic (), etc.
- Remember: adding a negative number is the SAME as subtracting a number.
|Shifting Functions Vertically (Up or Down)
- Up: to shift a graph up, increase the value of the y-coordinate for each point.
- Video of a quadratic function shifted up
- Down: to shift a graph down, decrease the value of the y-coordinate for each point.
- Video of quadratic function shifted down
- Examples: Shifting Graphs Vertically (Up or Down)
- To shift a graph vertically, add positive numbers (UP) or negative numbers (DOWN) to the right-hand side of its equation.
- Example: Quadratic
- Shifted UP by 2:
- Example: Linear
- Shifted DOWN by 4:
- Example: Quartic
- Shifted UP by 7:
|Shifting Functions Horizontally (Left or Right)
- To shift a graph horizontally, use this formula y = (x – value)
- Shift RIGHT: Subtracting a positive: (x – (+h)) becomes (x – h)
- Positive h (in parenthesis above) stands for the horizontal shift to the right
- Shift LEFT: Subtracting a negative (x – (-h)) becomes (x + h)
- Negative h (in the parenthesis above) stands for a horizontal shift to the left
- You will have to add parenthesis around the x-value and this new value.
- Example: Quadratic Function Shifts (of the parent function):
- Shifted LEFT by 5:
- Notice how the plus 5 is INSIDE the parenthesis, before the exponent (square)
- Shifting LEFT: (x + value). It’s the opposite of what you would normally think!
- Shifted RIGHT by 6:
- Notice that the minus 6 is INSIDE the parenthesis, before the exponent (square)
- Shifting RIGHT: (x – value). It’s the opposite of what you would normally think!
|Shifting BOTH: Vertically (Up or Down) AND Horizontally (Left or Right)
- Original parent function: black
- Shift Up and Right: red
- Shift Down and left: blue
- Notice how the red graph has shifted Down and to the Left
- Identify a point (the vertex is an easy one to find), then:
- Down by 2: add a negative to the end of the equation on the right side
- Left by 1: add a value to the x-value, inside parenthesis
- So, D is the answer:
Permanent link to this article: http://newvillagegirlsacademy.org/math/?page_id=2390