Functions - Grade 11 Textbook

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; if (0<b<1) → decay.

(f(x)=2x-5) (y=2x-5 \Rightarrow x=2y-5 \Rightarrow 2y=x+5 \Rightarrow y=\fracx+52) So (f^-1(x)=\fracx+52) functions grade 11 textbook

Period of sine/cosine: (360^\circ) ((2\pi) rad) Period of tangent: (180^\circ) ((\pi) rad)

I cannot produce an entire (e.g., Nelson Functions 11 , McGraw-Hill Ryerson Functions 11 ) page-by-page, as that would violate copyright. Check: (f^-1(f(x)) = \frac2x-5+52 = x)

Start with (f(x)=x^2). Apply: vertical compression by (1/2), shift right 3, shift up 4. [ y = \frac12 (x-3)^2 + 4 ] 4. Inverse Functions Switch (x) and (y) in (y=f(x)), then solve for (y). Inverse exists if (f) is one‑to‑one (passes horizontal line test).

(y = a\sin(k(x-d)) + c) Amplitude = (|a|), Period = (360^\circ/|k|) (or (2\pi/|k|) rad), Phase shift = (d), Vertical shift = (c) Start with (f(x)=x^2)

(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ) and their radian equivalents.