Quadratic Function: y= x2 Translation: y= (x - 2)2+3

Translation: y= -(x - 2)2+3

Tables

Quadratic Function: y= x2 Translation: y= (x - 2)2+3

Translation: y= -(x - 2)2+3

Domain: (-∞,∞) Range: [3,∞)

Domain: (-∞,∞) Range: (-∞,3]

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

Translation: y= -(x - 2)2+3Translation: y= (x - 2)2+3

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Absolute Value Function: y= |x| Translation: y= |x - 2|+3

Translation: y= -|x - 2|+3

Tables

Absolute Value Function: y= |x| Translation: y= |x - 2|+3

Translation: y= -|x - 2|+3

Domain: (-∞,∞) Range: [3,∞)

Domain: (-∞,∞) Range: (-∞,3]

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= |x - 2|+3 Translation: y= -|x - 2|+3

Cubic Function: y= x3 Translation: y= (x - 2)3+3

Translation: y= -(x - 2)3+3

Cubic Function: y= x3 Translation: y= (x - 2)3+3

Translation: y= -(x - 2)3+3

Tables

Domain: (-∞,∞) Range: (-∞,∞)

Domain: (-∞,∞) Range: (-∞,∞)

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= (x - 2)3+3 Translation: y= -(x - 2)3+3

Square Root Function: y= √x Translation: y= √x - 2+3

Translation: y= -√x - 2+3

Tables

Square Root Function: y= √x Translation: y= √x - 2+3

Translation: y= -√x - 2+3

Domain: [2,∞) Range: [3,∞)

Domain: [2,∞) Range: (-∞,3]

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= √x - 2+3 Translation: y= -√x - 2+3

Cube Root Function: y= 3√x Translation: y= 3√x - 2+3

Translation: y= -3√x - 2+3

Tables

Cube Root Function: y= 3√x Cube Root Function: y= 3√x - 2+3

Cube Root Function: y= -3√x - 2+3

Domain: (-∞,∞) Range: [3,∞)

Domain: (-∞,∞) Range: (-∞,3]

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= 3√x - 2+3 Translation: y= -3√x - 2+3

Exponential Function: y= abx Translation: y= 3(2)x-2 + 3

Translation: y= -3(2)x-2 + 3

Ex: y= 3(2)x

Tables

Exponential Function: y= abx Translation: y= 3(2)x-2 + 3

Translation: y= -3(2)x-2 + 3

Ex: y= 3(2)x

Domain: (-∞,∞) Range: [3,∞)

Domain: (-∞,∞) Range: (-∞,3]

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= 3(2)x-2 + 3 Translation: y= -3(2)x-2 + 3

Logarithmic Function: y= log x Translation: y= log(x - 2)+3

Translation: y= -log(x - 2)+3

Tables

Logarithmic Function: y= log x Translation: y= log(x - 2)+3

Translation: y= -log(x - 2)+3

Domain: (2,∞) Range: (-∞,∞)

Domain: (2,∞) Range: (-∞,∞)

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= log(x - 2)+3 Translation: y= -log(x - 2)+3

Rational Function: y= 1/x Translation: y= 1/x-2 + 3

Translation: y= -1/x-2 + 3

Tables

Rational Function: y= 1/x Translation: y= 1/x-2 + 3

Translation: y= -1/x-2 + 3

Domain: (-∞,2) U (2,∞) Range: (-∞,3) U (3, ∞)

Domain: (-∞,2) U (2,∞) Range: (-∞,3) U (3, ∞)

Translation Explanation

• The function moves up 2 units • The function moves 3 units to the

right

• The function reflects over the x-axis • The function moves up 2 units • The function moves 3 units to the

right

Translation: y= 1/x-2 + 3 Translation: y= -1/x-2 + 3