Grade 11 Functions

Functions and transformations

Transformations describe how one parent function becomes an entire family of related graphs.

y = a f (k (x - d)) + c

Transformation form

Factors, degree, leading coefficient, and multiplicity shape intercept and end behaviour.

f (x) = a (x - r_{1}) (x - r_{2})

Factored quadratic

Sine and cosine model repeating change through amplitude, period, phase, and midline.

y = a sin (k (x - d)) + c

Sinusoidal model

period = \frac{2 π}{∣ k ∣}

Radian period

A sequence tracks discrete change; arithmetic change adds while geometric change multiplies.

t_{n} = a + (n - 1) d

Arithmetic sequence

t_{n} = a r^{n - 1}

Geometric sequence