A car maintains a speed of 23 mi/h for five seconds it then accelerates to a speed of 46 mi/h in 5 seconds it maintains that speed for the next 5 seconds which graph shows the cars speed over time​

For this case we have three different functions in three different intervals.
 Let's write the function for each interval.
 We have:
 For t = [0,5]
 v (t) = 23 m / h
 For t = [5,10]
 v (t) - vo (t) = m * (t - to)
 m = (46-23) / (10-5)
 m = 4.6
 We choose an ordered pair:
 (to, vo (t))) = (5, 23)
 Substituting:
 v (t) - 23 = (4.6) * (t - 5)
 Rewriting:
 v (t) - 23 = (4.6) * (t - 5)
 v (t) = 4.6 * t - 23 + 23
 v (t) = 4.6 * t
 For t = [10, 5]
 v (t) = 46
 Answer:
 First graphic (from left to right)