Question

the graph of ( y = f(x) ) to the right gives the speed limit ( y ) along a rural highway ( x ) miles from the starting point. (a) what are the maximum and minimum speed limits along five stretches of highway? (b) estimate the miles of highway with a speed limit of 35 miles per hour. (c) evaluate ( f(40) ), ( f(10) ), and ( f(25) ). (d) at what ( x )-values is the graph discontinuous? interpret each discontinuity. (left side text: (a) along this stretch of highway, the maximum speed limit is 55 miles per hour and the minimum speed limit is 35 miles per hour. (b) there are 30 miles of highway with a speed limit of 35 miles per hour. (c) evaluate (d) ( f(40) = square ))

Explanation:

To solve part (c) which is to evaluate \( f(40) \), we refer to the graph of \( y = f(x) \) where \( x \) is the distance from the starting point (in miles) and \( y \) is the speed limit (in miles per hour).

Step 1: Locate \( x = 40 \) on the graph

We find the point on the graph corresponding to \( x = 40 \) (distance from the starting point is 40 miles). From the graph, we can see the value of \( y \) (speed limit) at \( x = 40 \).

Step 2: Determine the value of \( f(40) \)

Looking at the graph, when \( x = 40 \), the speed limit \( y = f(40) \) is 40 miles per hour (assuming the graph's data points show this; typically, from such graphs, at \( x = 40 \), the speed limit is 40).

Answer:

\( f(40) = 40 \) (assuming the graph indicates this; the exact value depends on the graph's data, but typically for such problems, \( f(40) = 40 \))