,

1. ©4 a2M011p3N wKuuYtSaX DSJoyfAtgw2a1rceV 0LPLHCy.9 j gAJlblm DrGiRgthEtnsy Zrnexs6eJrqvretdm.I 5 YMgagdief 1wvi3t4ho rIvnQfhiBnuiqtieZ 0CXa1lBc3uTl5ujsC.u Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____
Date________________
Average Rates of Change
For each problem, find the average rate of change of the function over the given interval.
1) y = x2
− x + 1; [0, 3]
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
2) y = −
1
x − 2
; [−3, −2]
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
For each problem, find the equation of the secant line that intersects the given points on the function.
3) y = −x2
+ x + 2; (−2, −4), (1, 2)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
4) y = −
1
x
; (1, −1), (3, −
1
3)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-1-

2. ©C Q2f0c1i3X QK3uhtZaS 5SBomf0t9wcaurLeq PLfLcCf.4 K mATlSlv 0raiegohLtlsl frDehsTeqrivZewdc.E U nM7aEdYeK swSiQtZhl DIfnXfAiEnEilt7eo 3CyaOlocouQluupsD.i Worksheet by Kuta Software LLC
For each problem, find the average rate of change of the function over the given interval.
5) y = x2
+ 2; [−2, −
3
2
] 6) y = 2x2
− 2x + 1; [−1, −
1
2
]
7) y = −
1
x + 2
; [−1, −
1
2
] 8) y = 2x2
+ x + 2; [0,
1
2
]
For each problem, find the equation of the secant line that intersects the given points on the function.
9) y = −x2
− 2; (1, −3), (3
2
, −
17
4 ) 10) y =
1
x + 3
; (−1,
1
2), (−
1
2
,
2
5)
11) y =
1
x − 1
; (−2, −
1
3), (−
3
2
, −
2
5) 12) y = −
1
x
; (1, −1), (3
2
, −
2
3)
Critical thinking question:
13) The police have accused a driver of breaking the speed limit of 60 miles per hour. As proof, they provide
two photographs. One photo shows the driver's car passing a toll booth at exactly 6 PM. The second
photo shows the driver's car passing another toll both 31 miles down the highway at exactly 6:30 PM.
Does the photo evidence prove that the driver broke the speed limit during this time?
-2-

3. ©n 02d0j1G3b LKfuottaV SSeonf1t7wHa4roeK 9LlLxC2.p m LAPlJl7 orUiSg8hktFsj 8rseksReDrrv1eadt.Q E IMWaBdte4 zwtiRtthV sIJnDfci9nSiltKel NCYaalLc7uTlUuBsV.Q Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____
Date________________
Average Rates of Change
For each problem, find the average rate of change of the function over the given interval.
1) y = x2
− x + 1; [0, 3]
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
2
2) y = −
1
x − 2
; [−3, −2]
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
1
20
For each problem, find the equation of the secant line that intersects the given points on the function.
3) y = −x2
+ x + 2; (−2, −4), (1, 2)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
y = 2x
4) y = −
1
x
; (1, −1), (3, −
1
3)
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
y =
1
3
x −
4
3
-1-

4. ©1 Q2g0z1s3f KKOuntway AStoNf9t2wHair9eA 5LDLkCz.L R 3A7lAlo frLixgbh8tSsp 3r2ebsUeXrAvrexdq.l G xMea8dvev hwZiStGh1 7IhnVf1iVnSiRtweT TCca0lWcVu8lYunso.b Worksheet by Kuta Software LLC
For each problem, find the average rate of change of the function over the given interval.
5) y = x2
+ 2; [−2, −
3
2
]
−
7
2
6) y = 2x2
− 2x + 1; [−1, −
1
2
]
−5
7) y = −
1
x + 2
; [−1, −
1
2
]
2
3
8) y = 2x2
+ x + 2; [0,
1
2
]
2
For each problem, find the equation of the secant line that intersects the given points on the function.
9) y = −x2
− 2; (1, −3), (3
2
, −
17
4 )
y = −
5
2
x −
1
2
10) y =
1
x + 3
; (−1,
1
2), (−
1
2
,
2
5)
y = −
1
5
x +
3
10
11) y =
1
x − 1
; (−2, −
1
3), (−
3
2
, −
2
5)
y = −
2
15
x −
3
5
12) y = −
1
x
; (1, −1), (3
2
, −
2
3)
y =
2
3
x −
5
3
Critical thinking question:
13) The police have accused a driver of breaking the speed limit of 60 miles per hour. As proof, they provide
two photographs. One photo shows the driver's car passing a toll booth at exactly 6 PM. The second
photo shows the driver's car passing another toll both 31 miles down the highway at exactly 6:30 PM.
Does the photo evidence prove that the driver broke the speed limit during this time?
Yes. The average rate of change is 62 mph, so the driver must have been breaking the speed
limit some of the time.
-2-
Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com