Functions Grade 11 Textbook -

(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)

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

(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)) functions grade 11 textbook

A population starts at 500, doubles every 4 hours. Model: (P(t) = 500 \cdot 2^t/4) where (t) in hours.

Find population after 10 hours: (P(10)=500\cdot 2^10/4=500\cdot 2^2.5=500\cdot 2^2\cdot 2^0.5=500\cdot 4\cdot \sqrt2\approx 500\cdot 5.657 = 2828) Inverse of exponential: (y = \log_b x \iff b^y = x) Domain: (x>0) Range: all real numbers Model: (P(t) = 500 \cdot 2^t/4) where (t) in hours

(t_n = ar^n-1) Sum of (n) terms: (S_n = \fraca(r^n-1)r-1, r\neq 1)

(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ) and their radian equivalents. r\neq 1) (0^\circ

| 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)) |