Horizontal Stretch
Key points
- Horizontal stretches are the opposite of vertical stretches, in which the graph becomes “wider” rather than “taller”.
- The x-values of the graph are multiplied by a constant, while the y values remain the same.
- Horizontal stretches are achieved by multiplying the variable by a constant 1/c.
Horizontal Stretches are graph transformations in which the inputs, or x values of a function are multiplied by a constant. This is the opposite of a vertical stretch.
- Visually, a horizontal stretch makes the graph appear wider.
- The graph stretches away from the y axis.
- With a constant c:
- y=(x/c)^2 is a horizontal stretch of the parent function y=x^2.
- The variable is being multiplied by 1/c.
- The constant is greater than 1, so the variable is being multiplied by a decimal (1/2 for example, in which c=2).
- y=(x/c)^2 is a horizontal stretch of the parent function y=x^2.
The greater the factor of multiplication, the wider the graph becomes.
- In a horizontal stretch, the x values are multiplied: (cx,y).
- A greater factor means the x value becomes greater, while the y value remains the same.
- Since the variable is being multiplied by 1/c, the smaller the fraction, the wider the graph.
- A greater factor means the x value becomes greater, while the y value remains the same.
- The purple curve (x/3) is wider than the green curve (x/2).
- If the constant is less than 1, then you are multiplying by a value greater than one, so it would be a horizontal compression, which is the same as a vertical stretch.
- Since vertical stretches and horizontal stretches are the opposite:
- A horizontal compression is the same as a vertical stretch.
- A horizontal stretch is the same as a vertical compression.
- Since vertical stretches and horizontal stretches are the opposite:
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