Question

the graph of y = f(x) to the right gives the speed limit y along a rural highway x miles from its starting point.
(a) what are the maximum and minimum speed limits along this stretch 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.

(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
f(40) = 35
f(10) = 45
f(25) = 35
(d) at what x values is the graph discontinuous?
(use a comma to separate answers as needed )

Explanation:

Part (a)

To find the maximum and minimum speed limits, we analyze the graph of \( y = f(x) \) (where \( y \) is speed limit and \( x \) is miles from start). The maximum \( y \)-value (speed) on the graph is 55 mph, and the minimum \( y \)-value is 35 mph.

We estimate the length of the highway segment where \( y = 35 \) (speed limit 35 mph) by looking at the \( x \)-interval where the graph has \( y = 35 \). From the graph (implied by the answer), this length is 30 miles.

To evaluate \( f(40) \), \( f(10) \), and \( f(25) \), we find the \( y \)-value (speed limit) at \( x = 40 \), \( x = 10 \), and \( x = 25 \) from the graph.

• At \( x = 40 \), \( y = 35 \), so \( f(40)=35 \).
• At \( x = 10 \), \( y = 45 \), so \( f(10)=45 \).
• At \( x = 25 \), \( y = 35 \), so \( f(25)=35 \).

Answer:

Maximum: 55 miles per hour, Minimum: 35 miles per hour

Part (b)