Moderate -0.8 This is a straightforward C1 question testing basic transformations and curve sketching. Part (i) requires simple sketching and solving 2x^4 = 2√x (which gives x=1). Parts (ii) and (iii) are standard textbook transformation exercises requiring only direct application of rules (horizontal translation and stretch), with no problem-solving or novel insight needed.
8. (i) Sketch the graphs of \(y = 2 x ^ { 4 }\) and \(y = 2 \sqrt { x } , x \geq 0\) on the same diagram and write down the coordinates of the point where they intersect.
(ii) Describe fully the transformation that maps the graph of \(y = 2 \sqrt { x }\) onto the graph of \(y = 2 \sqrt { x - 3 }\).
(iii) Find and simplify the equation of the graph obtained when the graph of \(y = 2 x ^ { 4 }\) is stretched by a factor of 2 in the \(x\)-direction, about the \(y\)-axis.
8. (i) Sketch the graphs of $y = 2 x ^ { 4 }$ and $y = 2 \sqrt { x } , x \geq 0$ on the same diagram and write down the coordinates of the point where they intersect.\\
(ii) Describe fully the transformation that maps the graph of $y = 2 \sqrt { x }$ onto the graph of $y = 2 \sqrt { x - 3 }$.\\
(iii) Find and simplify the equation of the graph obtained when the graph of $y = 2 x ^ { 4 }$ is stretched by a factor of 2 in the $x$-direction, about the $y$-axis.\\
\hfill \mbox{\textit{OCR C1 Q8 [9]}}