math final review

domain/range

100

f(x)= 1/x 

(-inf,0)U(0,inf) 

200

f(x)=sqrt(4x-5) 

[5/4, inf) 

300

f(x)=1/(sqrt(x²-9)) 

(-inf,-3)U(-3,3)U(3,inf) 

400

Find your domain 

f(x)= x/(x²-4) 

(-inf,-2)U(-2,2)U(2,inf) 

500

find domain 

f(x)=sqrt(16-x²) 

[-4,4]

solve for x

100

solve for x 

4(3x−5)=32

x=13/3

200

solve for x 

2x/5+3=7 

x=10 

300

sqrt(2x+1)=5 

x= 12

400

10^x+3=7 

x=(log (4)) / (log (10)) 

500

3(3^x+1)=27

x=(log(8))/(Log(3)) 

compositions

100

Compose f(g(x)) if f(x)=x^4 and g(x)=3x-9

f(g(x))=(3x-9)^4

200

Compose u(z(x)) if u(x)=u/12 and z(x)=9x+3

u(z(x))=(9x+3)/12

300

Compose a(b(x)) if a(x)=x^2-36 and b(x)=x^9

a(b(x))=x^18-36

400

Compose u(z(x)) if u(x)=8x^2 and z(x)=sqrt(x)

u(z(x))=8x

500

Compose f(g(x)) if f(x)=(x^2-12)/(8x) and g(x)=2x^2

f(g(x))=(4x^4-12)/(16x^2)

classify the function

100

Classify the function f(x)=100(2)^x.

Exponential.

200

Classify the function f(x)=x/4-120

Linear.

300

Classify the function f(x)=(8x)^(1/3).

Power Function.

400

Classify the function f(x)=1252/12^(t/5).

Exponential.

500

Classify the function f(x)=(x^2+8x)/x.

Linear. 

equivalent functions

100

Are (x-3)^2 and x^2-9 equivalent?

NO!!!!!!!! (x-3)^2=x^2-6x+9

200

Are the following equations equivalent? x^2−4x+4=0 and (x−2)^2=0

Yes.

300

Are (x+2)/(x-1) and (x-2)/(x+1) equivalent?

No.

400

Are (x^2−4)/(x-2) and x+2 equivalent?

Yes!

500

Are (x^2+2x)/(x^2-x) and (x+2)/(x-1) equivalent?

Yes.