Given \( I(x)=2 x+5 \) and \( g(x)=(2 x+5)+13 \), describe how the graph of \( g \) compares with the graph of \( f \). How does the graph of \( g \) compare with the graph of \( f \) ? A. The graph shifts 13 units to the right. B. The graph shifts 13 units down. C. The graph becomes steeper. D. The graph becomes less steep. E. The graph shifts 13 units up. F. The graph shifts 13 units to the left.

1. The function \( f(x)=2x+5 \) has a graph that is a straight line with slope \( 2 \) and \( y \)-intercept \( 5 \). 2. The function \( g(x) \) is given by \[ g(x) = (2x+5)+13. \] This can be rewritten as \[ g(x) = 2x + 5 + 13 = 2x + 18. \] 3. Since \( g(x) \) has the same slope of \( 2 \) as \( f(x) \), the steepness of the graph does not change. 4. The \( y \)-intercept of \( g(x) \) is \( 18 \) (as opposed to \( 5 \) for \( f(x) \)). This is because each point on the graph of \( f \) has been increased by \( 13 \) in the \( y \)-direction. 5. This represents a vertical shift upward by \( 13 \) units. Thus, the graph of \( g \) is identical to the graph of \( f \) except that it is shifted \( 13 \) units up. The answer is E.