(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ) and their radian equivalents.
(t_n = ar^n-1) Sum of (n) terms: (S_n = \fraca(r^n-1)r-1, r\neq 1)
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 functions grade 11 textbook
(f(x)=x^2+1), (g(x)=2x-3) Find ((f\circ g)(x) = f(g(x)) = (2x-3)^2 + 1 = 4x^2 -12x + 10) 3. Transformations of Functions Given (y = a,f(k(x-d)) + c):
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). Apply: vertical compression by (1/2), shift right 3,
Key: (b>0, b\neq 1) If (b>1) → growth; if (0<b<1) → decay.
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). Inverse exists if (f) is one‑to‑one (passes horizontal
(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))