algebra one

standard form

100

Y=3x+5

-3x+y=5

200

y-2=4(x+1)

 −4x+y=6

300

y=−2x−7

2x+y=−7

400

y=1/2x+6

−x+2y=12

500

2y=5x−3

−5x+2y=−3

Algebraic Proportions

100

x/3 = 8/12

x=2

200

x/5= 15/9

x=3

300

7/4=X/20

x=35

400

X/6=9/2

X=27

500

12/X = 4/10

X=30

Exponent Rules

100

4³ x 4² 

4⁵=1024 

200

10⁵/10³ =

10²=100

300

7⁰ =

1

400

(2⁴)²=

1

500

3^-2=

1/9

domain and range

100

f(x)=x+5f(x) 

• Domain: all real numbers

• Range: all real numbers

200

f(x)=x²

• Domain: all real numbers

• Range: y≥0y \ge 0y≥0 (0 and all positive numbers)

300

f(x)= 1/x-3

• Domain: all real numbers except 3
• Range: all real numbers except 0 

400

f(x)=xf sqrt(x)  

• Domain: x≥0x 
• Range: y≥0y 

500

x: 1, 2, 3, 4
f(x): 5, 7, 7, 10

• Domain: {1, 2, 3, 4}

• Range: {5, 7, 10}

Direct and Inverse Variation

100

If y varies directly with x, and  y=18 when x = 3 find k

k=y/x=18/3-6

200

y=kx. If k= 4 find y when x=7

y=4(7)=28

300

If y varies inversely with x, and y =10 when x=2=find k.

k=xy=10⋅2=20

400

 y=k/x, and k=36 Find y when x = 9

y=36/9=4

500

Which is inverse variation?

A) y=5x
B) y=12/x
C) y=x+3

it is   (because y =k/x)