Vertical Stretch
Key points
- Vertical stretches occur when a base graph is multiplied by a factor that is greater than 1.
- Multiplying the y values.
- Vertical compressions have a factor that is less than 1.
- Multiplying the y values.
- The greater the factor, the “taller” and “skinnier” the graph becomes.
Vertical Stretches are graph transformations in which the outputs of the function, or the y values, are multiplied by a constant.
- Visually, this graph appears as a stretch, in which the graph becomes taller and skinnier.
- With a constant c:
- y=cx^2 is a vertical stretch of the function y=x^2, by a factor of c.
- For a vertical stretch, the factor is always greater than 1.
- Vertical compressions have a factor less than 1.
The greater the factor of multiplication, the taller and skinnier the graph becomes. The opposite is true for a compression.
- In a vertical stretch, the y values are multiplied: (x,cy).
- A greater factor means the y value becomes greater, while the x value remains the same.
- The dark red graph has a greater factor (or coefficient) than the blue one, so it is taller.
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