1. **Stating the problem:** We are given a function $y=f(x)$ with one turning point at $(-6,-4)$. We need to find the coordinates of the turning point for the transformed functions: (a)(i) $y=f(x)+5$ (a)(ii) $y=f(3x)$ 2. **Understanding turning points:** A turning point occurs where the derivative of the function equals zero (critical point) and the function changes direction. 3. **For part (a)(i):** - The transformation is $y = f(x) + 5$, which shifts the function vertically upwards by 5 units. - The $x$-coordinate of turning points remains the same, but the $y$-coordinate increases by 5. - Therefore, the turning point coordinates are: $$(-6, -4 + 5) = (-6, 1)$$ 4. **For part (a)(ii):** - The transformation is $y = f(3x)$, which horizontally compresses the function by a factor of 3. - The turning point's $x$ coordinate changes since the input to $f$ is multiplied by 3. - If original turning point is at $x=-6$, then solving $3x = -6$ gives $x = -2$. - The $y$ value is $f(3x) = f(-6)$, which is $-4$. - Hence the turning point coordinates are: $$(-2, -4)$$ --- 5. **Summary of answers:** (a)(i): $(-6, 1)$ (a)(ii): $(-2, -4)$ 6. **Regarding part (b):** - The user has asked about the piecewise linear graph $y = g(x)$ shown, but no explicit question was given. - To help with part (b), please provide the exact question you want answered about $g(x)$.