Name _____________ Block ____ Chapter 8 TEST Review Due ____ My test date:
Select the function that matches the graph.
1. ______
2. ______
3. ______
4. ______
5. ______
Select from the following and place matching letter on the given line.
A.
f ( x) 
1
x
B.
f ( x) 
1
x4
C.
f ( x) 
1
x4
D.
f ( x) 
1
2
x4
E.
f ( x) 
1
2
x4
F.
f ( x) 
x
x 9
G.
f ( x) 
x2  x
x2
2
All.1 Simplifying Rational Expressions
Simplify each expression:
a)
x2  x  6
3x

x2  4 x  3 x2  x  2
15 x 2  12 x 15x 2  3x  12
b)

36 x  45
24 x  30
c)
2x  1 2x  1

x 1
x 1
12  3x 2 3x  4
d) 2

x  x6 x3
10 x3 y 5 4 xy
 3
7
2x
8x y
4x
2x

( x  4) ( x  3)
3x
6 7


x 1 2x x
𝑥+2
−2𝑥 − 1
− 2
2𝑥 − 2 𝑥 − 4𝑥 + 3
𝑥+1
6𝑥−18
𝑥
𝑥−3
4
𝑥−2
=
𝑥 2 −8𝑥−15
𝑥 2 +4𝑥
−1
𝑤+3
÷ 𝑥 2 − 𝑥 − 20
Graph:
𝑓(𝑥 ) =
−3
𝑥
Domain
Range
Vertical Asymptote
Horizontal Asymptote
x-intercept
y- intercept
Graph:
ℎ(𝑥 ) =
2x2
x−1
Domain
Range
Vertical Asymptote
Horizontal Asymptote
x-intercept
y- intercept
Graph: 𝑔(𝑥 )
=
Domain
Range
Vertical Asymptote
Horizontal Asymptote
x-intercept
y- intercept
3
x+4
−2
x 2  3x  1
Given the function: f(x) =
4 x2  9
Domain
Range
Vertical Asymptote
Horizontal
Asymptote
As x approached positive infinity,
What is the end behavior of this function?
Graph: 𝑔(𝑥 )
=
x2 −4
x2 +x−6
Domain
Range
Vertical Asymptote
Horizontal Asymptote
x-intercept
y- intercept
What is a hole in the graph??______________________________________
When is there a hole in the graph?? ________________________________
𝑓(𝑥) =
𝑥+3
𝑥2 + 4
Domain: ___________________________ VA: ____________________
Range: _____________________________ HA: ___________________
Name the range of 𝑓 (𝑥 ) =
−3
𝑥+2
+4
A.
(−∞, 4)(4, ∞)
B.
(4, ∞)
C.
(−∞, −2)(−2, ∞)
D.
(−2, ∞)
Which function does not have a vertical asymptote?
A.
C.
𝑓(𝑥 ) =
𝑓(𝑥 ) =
𝑥+3
B.
𝑥 2 −9
6x
D.
x3 +8
𝑓(𝑥 ) =
𝑓(𝑥 ) =
𝑥+5
𝑥 2 +3𝑥−10
𝑥 2 −4
x−2
Which of the numbered choices represents the missing expression?
?
2p − 1
=
6𝑝2 + 𝑝 − 15
2p − 3
A.
6𝑝2 + 𝑝 − 13
B.
6𝑝2 + 7𝑝 − 5
C.
12𝑝2 + 14𝑝 − 10
D.
6𝑝2 + 14𝑝 − 10
Graph:
𝑓(𝑥 ) =
Hole
Y - intercept
Vertical Asymptote
Horizontal
Asymptote
3x−12
𝑥 2 −2x−8
Find the inverse of function:
f ( x)  16 x 2  1, where x  0
Choose one
A.
B.
C.
D.
of these phrases to describe the roots of the equations shown:
Exactly 2 distinct real roots
Exactly 2 distinct imaginary roots
Exactly 3 distinct real roots
Exactly 1 real root and 2 distinct imaginary roots
Place choice A – D on line
x2  2 x  3  0
__________
3x 2  5  0
__________
2 x3  2 x 2  3  0
__________
Add and subtract the following rational expressions, as indicated, and simplify answers.
5
3
3  4n
2
x
1



2
2
a a 1
n  3n  10 n  5
x  x  30 x  5
x
3

2
x  9 x  x  3
m2
m2  8
3
4
p2  5

 2
p  1 2p  6 p  2p  3
j2  7 j  6
12 j 3  14 j 2  10 j
2y 2  9y  18
4 y 2  6y
Name _________________ Block ______ 8.1Variation Review Due ______
Select the equation that represents a direct variation.
A.
𝑦 =𝑥+5
C.
𝑥=
3
𝑦
𝑦
B.
𝑘=
D.
𝑥𝑦 = 8
𝑥
𝑇ℎ𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑎𝑛 𝑖𝑡𝑒𝑚 𝑖𝑛 𝑒𝑢𝑟𝑜𝑠 𝑒 𝑣𝑎𝑟𝑖𝑒𝑠 𝑑𝑖𝑟𝑒𝑐𝑡𝑙𝑦 𝑎𝑠 𝑡ℎ𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑡𝑒𝑚 𝑖𝑛 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 𝑑, 𝑎𝑛𝑑
𝑒 = 3.85 𝑒𝑢𝑟𝑜𝑠 𝑤ℎ𝑒𝑛 𝑑 = $5.00. 𝐹𝑖𝑛𝑑 𝑑 𝑤ℎ𝑒𝑛 𝑒 = 10.00 𝑒𝑢𝑟𝑜𝑠.
𝑇ℎ𝑒 𝑣𝑜𝑙𝑢𝑚𝑒 𝑉 𝑜𝑓 𝑎 𝑐𝑜𝑛𝑒 𝑣𝑎𝑟𝑖𝑒𝑠 𝑗𝑜𝑖𝑛𝑡𝑙𝑦 𝑎𝑠 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑎𝑠𝑒 𝐵 𝑎𝑛𝑑 𝑡ℎ𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 ℎ, 𝑎𝑛𝑑
𝑉 = 12 𝜋𝑓𝑡 3 𝑤ℎ𝑒𝑛 𝐵 = 9𝜋 𝑓𝑡 3 𝑎𝑛𝑑 ℎ = 4 𝑓𝑡. 𝐹𝑖𝑛𝑑 𝑏 𝑤ℎ𝑒𝑛 𝑉 = 24𝜋 𝑓𝑡 3 𝑎𝑛𝑑 ℎ = 9 𝑓𝑡
𝑦 𝑣𝑎𝑟𝑖𝑒𝑠 𝑖𝑛𝑣𝑒𝑟𝑠𝑒𝑙𝑦 𝑎𝑠 𝑥, 𝑎𝑛𝑑 𝑦 = 4 𝑤ℎ𝑒𝑛 𝑥 = 5.
𝑊𝑟𝑖𝑡𝑒 𝑎𝑛𝑑 𝑔𝑟𝑎𝑝ℎ 𝑡ℎ𝑒 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛
Select all equation(s) that represent this situation? Circle your choices
A car’s stopping distance, d, varies directly with the speed it travels, s, and
inversely with the friction value of the road surface, f.
df  ks
dk 
ds  kf
k
s
f
df
s
d  ksf
d
ks
f
How do you verify that a t-chart is direct? ___________ or an inverse? ___________
State whether each equation represents a direct, inverse, or joint variation.
Name the constant of variation
𝑥
3
𝑦 = 2𝑥
=𝑦
𝑥𝑦 = 12
D = 4 𝑔ℎ
5
Is 𝑦 = 3𝑥 + 5 𝑎 𝑑𝑖𝑟𝑒𝑐𝑡 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛? ______ WHY OR WHY NOT_________________
Write an equation for and solve each of the following word problems.
1. The cost, c, in cents of lighting a 100-watt bulb varies directly as the time, t, in hours, that
the light is on. The cost of using the bulb for 1,000 hours is $0.15. Determine the cost of
using the bulb for 2,400 hours.
2.
The force needed to keep a car from skidding on a curve varies directly as the weight of the
car and the square of the speed and inversely as the radius of the curve. Suppose a 3,960
lb. force is required to keep a 2,200 lb. car traveling at 30 mph from skidding on a curve of
radius 500 ft. How much force is required to keep a 3,000 lb. car traveling at 45 mph from
skidding on a curve of radius 400 ft.?