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Describe the differences to show the change from f(x)=x

to g(x)=2x + 8
(4 points)
The slope
by a factor of 2.

The graph moved
the y-axis 8 units.

1 answer

To describe the changes from the function \( f(x) = x \) to \( g(x) = 2x + 8 \), we'll break down the differences:

  1. Slope Change:

    • The slope of \( f(x) = x \) is 1.
    • The slope of \( g(x) = 2x + 8 \) is 2.
    • Therefore, the slope increased by a factor of 2. This means that for every unit increase in \( x \), \( g(x) \) increases by 2 units instead of just 1.

  2. Y-Intercept Change:

    • The y-intercept of \( f(x) = x \) is 0 (it crosses the y-axis at (0,0)).
    • The y-intercept of \( g(x) = 2x + 8 \) is 8 (it crosses the y-axis at (0,8)).
    • Thus, the graph moved up 8 units on the y-axis. This means that the entire graph of the function has been shifted vertically upward.

In summary:

  • The slope increased from 1 to 2 (by a factor of 2).
  • The graph moved up 8 units on the y-axis.