Questions: Stretch the graph vertically by a factor of 8. Shrink the graph horizontally and vertically by a factor of 8. Stretch the graph horizontally and vertically by a factor of 8. Shrink the graph horizontally by a factor of 8. Stretch the graph horizontally by a factor of 8.

Solution Steps

To solve the problem of transforming the function \( y = 8f\left(\frac{1}{8}x\right) \), we need to understand the effects of the transformations described:

1. Vertical Stretch by a Factor of 8: The coefficient 8 outside the function \( f \) indicates a vertical stretch by a factor of 8.
2. Horizontal Shrink by a Factor of 8: The argument \( \frac{1}{8}x \) inside the function indicates a horizontal stretch by a factor of 8 (since \( x \) is divided by 8, it effectively stretches the graph horizontally).

The other transformations mentioned in the text are not applicable to the given function form.

The given function transformation is \( y = 8f\left(\frac{1}{8}x\right) \). This involves two main transformations:

• Vertical Stretch: The factor of 8 outside the function \( f \) indicates that the graph of the function is stretched vertically by a factor of 8.
• Horizontal Stretch: The argument \( \frac{1}{8}x \) inside the function indicates that the graph is stretched horizontally by a factor of 8. This is because dividing \( x \) by 8 effectively stretches the graph along the x-axis.

• Vertical Stretch: For any point \((x, f(x))\) on the original graph, the new point on the transformed graph will be \((x, 8f(x))\). This means that the y-values are multiplied by 8.
• Horizontal Stretch: For any point \((x, f(x))\) on the original graph, the new point on the transformed graph will be \((8x, f(x))\). This means that the x-values are multiplied by 8.

The combined effect of these transformations on the function \( f(x) \) results in the new function \( y = 8f\left(\frac{1}{8}x\right) \). This means:

• The graph is stretched vertically by a factor of 8.
• The graph is stretched horizontally by a factor of 8.

Final Answer