(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ) and their radian equivalents.
However, I put together a structured “paper” / study guide that mirrors the key topics, learning objectives, and practice problems you would find in a typical Grade 11 Functions textbook (Ontario curriculum MCR3U).
| Parameter | Effect | |-----------|--------| | (a) | vertical stretch ((|a|>1)) or compression ((0<|a|<1)), reflection in x‑axis if (a<0) | | (k) | horizontal stretch/compression, reflection in y‑axis if (k<0) | | (d) | horizontal shift (right if (d>0)) | | (c) | vertical shift (up if (c>0)) | functions grade 11 textbook
Below is a summary + original problems. Grade 11 Functions – Study Paper Topics: Characteristics of functions, domain/range, transformations, inverse functions, exponential functions, trigonometric functions, sequences & series. 1. Function Basics Definition: A function (f) pairs each element (x) in the domain with exactly one element (y) in the range.
Key: (b>0, b\neq 1) If (b>1) → growth; if (0<b<1) → decay. Grade 11 Functions – Study Paper Topics: Characteristics
(y = 3\cos(2x - \pi) + 1) Rewrite: (y = 3\cos(2(x - \pi/2)) + 1) Amplitude 3, Period (360/2=180^\circ) ((\pi) rad), Phase shift (\pi/2) right, Vertical shift 1 up. 8. Sequences & Series Arithmetic sequence: (t_n = a + (n-1)d) Sum of (n) terms: (S_n = \fracn2(2a + (n-1)d))
Check: (f^-1(f(x)) = \frac2x-5+52 = x). General form: (f(x) = a\cdot b^k(x-d) + c) Key: (b>0, b\neq 1) If (b>1) → growth;
(y = a\sin(k(x-d)) + c) Amplitude = (|a|), Period = (360^\circ/|k|) (or (2\pi/|k|) rad), Phase shift = (d), Vertical shift = (c)
I cannot produce an entire (e.g., Nelson Functions 11 , McGraw-Hill Ryerson Functions 11 ) page-by-page, as that would violate copyright.
(t_n = ar^n-1) Sum of (n) terms: (S_n = \fraca(r^n-1)r-1, r\neq 1)