Final Review 2026

Rational Equations

100

3/(x+2)=1/(x+2)-1

x=-4

200

1=1/(5v)-1/5

x=1/6

300

1+1/(2x+1)=6/(2x+1)

x=2

400

3/(x^2-5x+6)=1/(x^2-5x+6)-1/(x-3)

x=0

500

1/(x^2+5x-6)-2/(x-1)=1/(x+6)

x=-12

Quadratics

100

x^2=-11x+60

x=4, -15

200

6x^2=96

x=+-4

300

x^2+5x-17=0

x=(-5+-sqrt(93))/2

400

3x^2+7x-48=0

x=3,-16/3

500

9x^2+12=3n

x=(1+-isqrt(47))/6

Radical Equations

100

sqrt(10x+4)=8

x=6

200

-7sqrt(13-x)=-14

x=9

300

6+sqrt(3x-8)=10

x=8

400

sqrt(2x-3)=x-1

x=2

500

sqrt(3x-8)=x-4

x=8

Domain and Range

100

f(x)=(x-2)^2-3

domain: all real numbers

range:  y>=-3 

200

f(x)=-2(x-1)^2+4

domain: all real numbers

range:  y<=4 

300

f(x) = sqrt(x-1)

domain:  x>=1 

range:  y>=0 

400

f(x) = 2sqrt(x)+3

domain:  x>=0 

range: y>=3 

500

f(x) = 1/3sqrt(x+2)+5

domain: x>=-2 

range: y>=5 

Logs and Exponents

100

4x^(4/3)+3=67

x=+-8

200

64=(5x-4)^(3/2)

x=4

300

log_5(7)+log_5(-x)=log_5(41)

x=-41/7

400

log_4(x-3)+log_4(7)=1

x=25/7

500

log_4(-2x)-log_4(2)=1

x=-4