Function Operations
h(x)=3x+3
g(x)=-4x+1
Find (h+g)(10)
find the hole, horizontal, and vertical asymptotes of 4/x-3
hole:0,3
horizontal:0
vertical:1
Solve by substitution
y = 4x − 9
y = x − 3
(2, −1)
Find the Vertical Asymptote
f(x)=1/x+2
x = −2
1 / x − 4 ⋅ −x 2 + 9x − 20 / x + 2
(x − 5) ⋅ −1 x + 2 ; {4, −2}
g(x)=2x-5
h(x)=4x+5
Find g(3)-h(3)
=-16
Identify the domain and range of y=log6(x-1)-5
domain:x>1
range: all real numbers
Solve by substitution
−7x + 2y = 18
6x + 6y = 0
(−2, 2)
Find Horizontal Asymptote
f(x)=4x+5x/ x+1
y=4
6r / r + 8 ⋅ 8r + 64 / 8
6r; {−8}
g(a)=2a-1
h(a)=3a-3
Find (gxh)(-4)
=135
Identify the domain and range of log5(x-1)+3
domain:x>1
range:all real numbers
Solve by elimination
8x − 6y = −20
−16x + 7y = 30
(−1, 2)
Find hole
f(x)=x^2−9x^2/ x^2−3x
(3,2)
x^2 − 1 / x − 1 ⋅ 1 / x − 3
x + 1 / x − 3 ; {1, 3}
g(a)=3n+2
h(a)=2n2+5
41
Identify the domain and range of y=log4(3x+11)-5
domain: x>-11/3
range:all real number
− 5/7 − 11/7 x = −y
2y = 7 + 5x
(−3, −4)
Find simplified version
f(x)=x^2+6x+9x / x^2−9
f(x)=(x+3)^2 / (x+3)(x−3)
9r + 90 / 4 ÷ 9r + 90 / 4r 2
r 2 ; {0, −10}
f (x) = 4x − 3 g(x) = x 3 + 2x Find ( f − g)(4)
g(a) = 3a + 2 f (a) = 2a − 4 Find ( g f ) (3)
-59
11/2
Find domain and Range
y = log 6 (x − 1) − 5
y = log 4 (x + 2) + 1
Domain: x > 1 Range: All reals
Domain: x > −2 Range: All reals
Solve by elimination
0 = −2y + 10 − 6x
14 − 22y = 18x
−4y − 11x = 36
20 = −10x − 10y
(2, −1)
(−4, 2)
Find hole
f(x)=x^2+3x+2 / 5x+5
f(x)=x^3−1 / x^2−1
(−1,1/5)
(1,3/2)
n^2 − 9n − 10 / n + 1 ÷ n + 3 / n + 10
4 / 20x − 12 ÷ 1 / 20x^2 − 12x
(n + 10)(n − 10) / n + 3 ; {−1, −10, −3}
4x;{3/5 , 0}