Question

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.

Answer 1

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.