Transformation Rules

10 Grade

f(x) + a

up “a” units (y)

f(x) - a

down “a” units (y)

f(x - a)

right “a” units (x)

f(x + a)

left “a” units (x)

(a)(f(x))

vertical dilation (y)

• | a | < 1 - vertical shrink

• | a | > 1 - vertical stretch

-f(x)

reflect over the x-axis (y)

f(ax)

horizontal dilation (x)

• | a | > 1 - horizontal compression → ←

• | a | < 1 - horizontal stretch ← →

• To perform a horizontal dialation, we divide original x-values by “a”

f(-x)

reflection over y-axis (x)

Linear Function

Parent Function: f(x) = x

Characteristics:

• Domain (-∞, ∞)

• Range (-∞, ∞)

• Slope: 1

• y-intercept: y = 0

• x-intercept: x=0

Quadratic Function

Parent Function: f(x) = x²

Characteristics:

• Domain: (-∞, ∞)

• Range: [0, ∞)

• Axis of Symmetry: x = 0

• Vertex: (0,0)

• y-intercept: y = 0

• x-intercept: x = 0

Cubic Function

Parent Function: f(x) = x³

Characteristics:

• Domain: (-∞,∞)

• Range (-∞, ∞)

• y-intercept: y = 0

• x-intercept: x = 0

Absolute Value Function

Parent Function: f(x) = |x|

Characteristics:

• Domain: (-∞, ∞)

• Range: [0,∞)

• Axis of Symmetry: x = 0

• Vertex: (0,0)

• y-intercept: y = 0

• x-intercept: x = 0

Square Root Function

Parent Function: f(x) = √x

Characteristics:

• Domain [0, ∞)

• Range: [0,∞)

• y-intercept: y = 0

• x-intercept: x = 0

Cube Root Function

Parent Function: f(x) = ∛x

Characteristics:

• Domain: (-∞, ∞)

• Range: (-∞, ∞)

• y-intercept: y = 0

• x-intercept: x = 0

Exponential Function

Parent Function: f(x) = b^x, where b > 1

Characteristics:

• Domain: (-∞,∞)

• Range: (0, ∞)

• y-intercept: y = 1

• x-intercept: none

• Horizontal Asymptote: y = 0