The function $\mathrm{f}$ is defined by \[\mathrm{f}(x) = \begin{cases} x+4 & \text{for } -4 \le x

Question

The function $\mathrm{f}$ is defined by $$\mathrm{f}(x) = \begin{cases} x+4 & \text{for } -4 \le x < -1, \ x^2+2 & \text{for } -1 \le x < 2. \end{cases}$$ It is given that $\mathrm{f}(x) = \mathrm{f}(x+6)$ for all real values of $x$. Sketch the graph of $y = \mathrm{f}(x)$ for $-6 \le x < 6$.[3] Hence sketch the graph of $y = 2\mathrm{f}(x-1)$ for $-6 \le x < 6$.[3]

Accepted Answer

(a) Period-6 sketch shown on $-6\le x<6$. (b) Right translation 1 and vertical stretch factor 2; transformed sketch shown, with lower jump endpoints included and upper endpoints excluded.

2025 TMJC P2 Q3

2025 TMJC P2 Q3

Solution:

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