1.factor denominator with box method 

2.Factored denominator: (2x-1) (x+1)

3. 2x-1=0; x+1=0; x=1/2; x= -1

4. D: [0, 1/2) U (1/2, ∞), R: (-∞,∞)

f(x)={^{5 if x ≤ 2 ; 2x-3 if x > 2 }}

f(-3)=

f(0)=

f(2)=

f(3)=

f(5)=

which is the open dot?

f(-3)=5

f(0)=5

f(2)=5

f(3)=2(3)-3=3

f(5)=2(5)-3=7

If f(2)=5 is put in the wrong equation( 2x-3) it is the open dot 

Inverse function of:

 f(x)=4x+7

y=f(x)

y=4x+7

y-7=4x

x=y-7÷4

find- f0g; gof; fof; gog

f(x)= x² 

g(x)= x+1

(fog) (x)= (x+1)²

(gof) (x)=x² +1

(fof) (x)= x⁴

(gog) (x)= x+2

1: Take the square root of each side

2: Factoring

3: Quadratic formula

4: Graphing

method 1:

x² - 5=0

9x² = 25

x²-5=0; x2=5 ; √x²=√5; x=⁺_-√5

 9x²=25; √9x²=√25; 3x=5; x= ⁺_- 5/3

Method 2:

x²+5x-24=0

x²+4x=32

x²+5x-24=0; (x-3)(x+8) (box method); x-3=0; x=3; x+8=0; x=-8; x=3 or x=-8

x²+4x=32;x²+4-32=0; (x-4)(x+8)(box method); x-4=0; x=4; x+8=0; x=-8; x=4 or x=-8

Method 3:

3(a)x²-5(b)x-1(c)=0

x=b+_-√b²-4ac÷2(a)

1: put i equation into y=

2: Fix window if neccessary

3: 2nd calc Maximum (4)

radicals w/exponents:

√a²×b⁶

³√a²×b  × ³√a⁴×b

√a²×b⁶; a×b³

³√a²×b  × ³√a⁴×b;³√a⁶×b²; a² ×b^2/3

Radical factorization:

√80

combining radicals

√32+√200= √16×2+√100×2

sin=y

cos=x

tan=y/x

csc=1/y

sec=1/x 

cot=x/y

calculator for inverses:

1/sin= csc

1/cos=sec

1/tan=cot

0; sin0=0; cos0=1; tan0=0; csc0=undefined; sec0=1;cot0=undeifined

∏/3 (1/2, √3/2)

∏/4(√2/2,√2/2)

∏/6(√3/2, 1/2)

∏/2(0, 1)