Moderate -0.8 This is a straightforward transformation question requiring knowledge of how stretches affect function equations. Students need to apply the standard rules: x → 4x for the x-stretch and y → 2y for the y-stretch, then rearrange. While it requires careful algebraic manipulation, it's a routine textbook exercise with no problem-solving insight needed, making it easier than average.
The curve \(y = \sqrt{2x - 1}\) is stretched by scale factor \(\frac{1}{4}\) parallel to the \(x\)-axis and by scale factor \(\frac{1}{2}\) parallel to the \(y\)-axis.
Find the resulting equation of the curve, giving your answer in the form \(\sqrt{ax - b}\) where \(a\) and \(b\) are rational numbers.
[3]
The curve $y = \sqrt{2x - 1}$ is stretched by scale factor $\frac{1}{4}$ parallel to the $x$-axis and by scale factor $\frac{1}{2}$ parallel to the $y$-axis.
Find the resulting equation of the curve, giving your answer in the form $\sqrt{ax - b}$ where $a$ and $b$ are rational numbers.
[3]
\hfill \mbox{\textit{SPS SPS FM 2024 Q4 [3]}}