A population starts at 500, doubles every 4 hours. Model: (P(t) = 500 \cdot 2^t/4) where (t) in hours.
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). functions grade 11 textbook
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). A population starts at 500, doubles every 4 hours
| 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)) | Start with (f(x)=x^2)
(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)