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Definition
no negatives allowed in a square root |
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Definition
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: (-∞,∞) |
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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? |
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Definition
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 |
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Inverse function of:
f(x)=4x+7
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Definition
y=f(x)
y=4x+7
y-7=4x
x=y-7÷4 |
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vertex formula for quadratic equations |
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Definition
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find- f0g; gof; fof; gog
f(x)= x2
g(x)= x+1 |
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Definition
(fog) (x)= (x+1)2
(gof) (x)=x2 +1
(fof) (x)= x4
(gog) (x)= x+2 |
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4 methods to solving quadratic equations |
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Definition
1: Take the square root of each side
2: Factoring
3: Quadratic formula
4: Graphing |
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standar equation for quadratics |
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Definition
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method 1:
x2 - 5=0
9x2 = 25 |
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Definition
x2-5=0; x2=5 ; √x2=√5; x=+-√5
9x2=25; √9x2=√25; 3x=5; x= +- 5/3 |
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Method 2:
x2+5x-24=0
x2+4x=32 |
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Definition
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 |
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Method 3:
3(a)x2-5(b)x-1(c)=0
x=b+-√b2-4ac÷2(a) |
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Definition
x=5+-√(-5)2-4(3)(-1)÷2(3);x=5+-√37/6 |
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Definition
1: put i equation into y=
2: Fix window if neccessary
3: 2nd calc Maximum (4) |
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radicals w/exponents:
√a2×b6
3√a2×b × 3√a4×b |
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Definition
√a2×b6; a×b3
3√a2×b × 3√a4×b;3√a6×b2; a2 ×b2/3 |
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Definition
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Radical factorization:
√80 |
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Definition
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combining radicals
√32+√200= √16×2+√100×2 |
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Definition
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sin=y
cos=x
tan=y/x
csc=1/y
sec=1/x
cot=x/y |
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Definition
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calculator for inverses:
1/sin= csc
1/cos=sec
1/tan=cot |
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Definition
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Definition
0; sin0=0; cos0=1; tan0=0; csc0=undefined; sec0=1;cot0=undeifined
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Definition
∏/3 (1/2, √3/2)
∏/4(√2/2,√2/2)
∏/6(√3/2, 1/2)
∏/2(0, 1) |
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