Describe the change from f(x)=x to g(x)=2x+8 .(2 points) The slope by a factor of 2. The graph moves the y-axis 8 units.

Answer 1

The change from \( f(x) = x \) to \( g(x) = 2x + 8 \) involves both a change in slope and a vertical shift.

1. Slope Change: The function \( f(x) = x \) has a slope of 1, while \( g(x) = 2x + 8 \) has a slope of 2. This means that the graph of \( g(x) \) rises twice as steeply as the graph of \( f(x) \). Therefore, the slope increases by a factor of 2.

2. Vertical Shift: The constant term in \( g(x) \) is +8, which indicates that the graph of \( g(x) \) is shifted vertically upward by 8 units compared to \( f(x) \). This movement affects where the line intersects the y-axis.

In summary, transitioning from \( f(x) = x \) to \( g(x) = 2x + 8 \) means that the slope is increased by a factor of 2, and the graph is shifted upwards by 8 units along the y-axis.