The graph of `y=f(x)`, where `f:[0,2 \pi] \rightarrow R, f(x)=2 \sin(2x)-1`, is shown below.
- On the axes above, draw the graph of `y=g(x)`, where `g(x)` is the reflection of `f(x)` in the horizontal axis. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- Find all values of `k` such that `f(k)=0` and `k \in[0,2 \pi]`. (3 marks)
--- 5 WORK AREA LINES (style=lined) ---
- Let `h: D \rightarrow R, h(x)=2 \sin(2x)-1`, where `h(x)` has the same rule as `f(x)` with a different domain.
- The graph of `y=h(x)` is translated `a` units in the positive horizontal direction and `b` units in the positive vertical direction so that it is mapped onto the graph of `y=g(x)`, where `a, b \in(0, \infty)`.
-
- Find the value for `b`. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Find the smallest positive value for `a`. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Hence, or otherwise, state the domain, `D`, of `h(x)`. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Find the value for `b`. (1 mark)