Algebra II 8

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y = 48 / x inverse

y = ½ x direct

+3 means neither

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y = k/x 6 = k/2 12 = ky = 12 / 4 y = 3

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6

Varies means “=a”

y = ax/z2

z = ax2yy = axz

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Stretches vertically by factor of 2Moves left 3Moves up 4

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Vertical: 3x – 6 = 0 3x = 6 x = 2Horizontal: y = (2*1000000)/(3*1000000 – 6) y = 2/3

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AsymptotesVertical: x + 3 = 0 x = -3Horizontal: y = 2/(1000000 + 3) + 4 y = 4

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Vertical: x2 – 1 = 0 x2 = 1 x = ±1Horizontal: y = (2(1000000)2 + 1000000)/(10000002 -1) y = 2

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Vertical: x2 – 1 = 0 x2 = 1 x = ±1Horizontal: y = (2(1000000)2 + 1000000)/(10000002 -1) y = 2

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((x-6)(x+1))/((x-1)(x+1)) (x-6)/(x-1)

(x(x+3)(x+2))/(x2(x+2)) (x+3)/x

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(-3x(9x2-1))/((3x+1)(x-1)) * ((3x-1)(x-1)) (-3x(3x-1)(3x+1)(3x-1)(x-1))/(3x(3x+1)(x-1)) -(3x-1)2

(x+2)/((3x+2)(9x2-6x+4)) * (9x2-6x+4)/1 (x+2)/(3x+2)

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3/(4x-8) * (x2+x-6)/(x2+3x) 3/(4(x-2)) * ((x-2)(x+3))/(x(x+3)) 3/(4x)

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-4/(2x) -2/x

(3x+6)/(x-4)

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4

3𝑥2+

𝑥

3𝑥2 2𝑥 + 1→

4 2𝑥 + 1

3𝑥2 2𝑥 + 1+

𝑥

3𝑥2 2𝑥 + 1→

9𝑥 + 4

3𝑥2 2𝑥 + 1

𝑥 + 1

𝑥 + 3 𝑥 + 3–

1

𝑥 + 3 𝑥 − 3→

𝑥 + 1 𝑥 − 3

𝑥 + 3 2 𝑥 − 3−

𝑥 + 3

𝑥 + 3 2 𝑥 − 3

→𝑥2 – 2𝑥 – 3

𝑥 + 3 2 𝑥 − 3–

𝑥 + 3

𝑥 + 3 2 𝑥 − 3→

𝑥2 − 3𝑥 − 6

𝑥 + 3 2 𝑥 − 3

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3𝑥 − 4

1𝑥 − 4 +

3𝑥 + 1

→

3𝑥 − 4

1 𝑥 + 1𝑥 − 4 𝑥 + 1

+3 𝑥 − 4

𝑥 − 4 𝑥 + 1

→

3𝑥 − 4

𝑥 + 1𝑥 − 4 𝑥 + 1

+3𝑥 − 12

𝑥 − 4 𝑥 + 1

→

3𝑥 − 44𝑥 − 11

𝑥 − 4 𝑥 + 1

→3

𝑥 − 4⋅𝑥 − 4 𝑥 + 1

4𝑥 − 11

→3 𝑥 + 1

4𝑥 − 11

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(3(2x))/x – 2x/2 = (12(2x))/x 6 – x = 24 -x = 18 x = -18

5x = 4(x+1) – 5 5x = 4x + 4 – 5 x = -1Check answer: can’t divide by -1 so NO SOLUTION

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(3x-2)/(x-2) = 6/((x-2)(x+2)) + 1 (3x-2)(x+2) = 6 + (x-2)(x+2) 3x2 + 4x – 4 = 6 + x2 –4 2x2 + 4x – 6 = 0 x2 + 2x – 3 = 0 (x – 1)(x + 3) = 0 x = 1, -3

3/(x(x+4)) = 1/(x+4) 3 = x

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