How do you write an equation that represents a vertical stretch of the function y = x by a factor of 6?

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To express the vertical stretch of the function y = x by a factor of 6, you need to multiply the output (y-value) of the function by 6. This means that for every value of x, the corresponding value of y will be increased by a factor of 6.

The original function can be represented as:

y = x

To implement the vertical stretch, you modify the equation as follows:

y = 6x

This new equation, y = 6x, reflects that for any given x, the value of y is now six times larger than it was in the original function. So, if you were to input a value for x, you would multiply that value by 6 to get the new y value.

For example:

  • If x = 1, then y = 6 * 1 = 6.
  • If x = 2, then y = 6 * 2 = 12.

This transformation effectively stretches the graph of the original function vertically by a factor of 6, making it taller while keeping the same slope.

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