stretch factor
[stretch factor|stretch factor] is a scalar value that determines the vertical scaling of a function.
Definition
stretch factor is a scalar value that determines the vertical scaling of a function. A negative value reflects the graph over the x-axis.
Mechanism
stretch factor To determine the stretch factor, another clear point on the graph, such as the y-intercept (0, -2), can be used. Rewriting the equation into standard form reveals that the stretch factor matches the coefficient 'a' in the original quadratic. The process involves finding the same value through different points, ensuring consistency in the form.
Effects
stretch factor To determine the stretch factor, we utilize another point on the graph. The y-intercept may be easiest for this purpose. Using any other point on the graph can help identify the stretch factor. This method allows the stretch factor to be calculated based on coordinate values. The stretch factor influences how the graph's shape is transformed.
Examples
stretch factor To determine the stretch factor, a clear point on the graph like the y-intercept (0, -2) can be used. The stretch factor is calculated by finding the relationship between this point and the graph's intercept. Using such a point helps identify the stretch factor through its coordinates. The y-intercept provides a specific value for calculating the stretch factor. This method ensures the stretch factor is derived accurately from the graph's data.
Also Reflection
stretch factor The stretch factor is also noted to influence vertical transformations. A negative stretch factor introduces a reflection about the x-axis. This dual effect is specifically tied to the vertical direction. The relationship between stretch factor and reflection is a key characteristic. The term 'also' highlights an additional property of the stretch factor.
Stretch Based
stretch factor The stretch factor is used when the stretch based on width cannot be determined from the graph. It requires inputting a known pair of x and f(x) values to solve for the factor. This method allows calculation of the stretch factor without relying on graphical width measurements.
Vertical Stretch
stretch factor refers to the vertical stretch applied to a function. A negative stretch factor indicates a reflection over the x-axis. This factor determines the magnitude of the vertical scaling.