Moderate -0.8 This is a straightforward question requiring students to form two composite functions (|x+1| and |x|+1) and sketch their graphs. It involves routine application of function composition and standard transformations of the modulus function (horizontal vs vertical translation), which are core C3 skills with no problem-solving or novel insight required.
2 Given that \(\mathrm { f } ( x ) = | x |\) and \(\mathrm { g } ( x ) = x + 1\), sketch the graphs of the composite functions \(y = \mathrm { fg } ( x )\) and \(y = \operatorname { gf } ( x )\), indicating clearly which is which.
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\text{fg}(x) = |x+1|$, $\text{gf}(x) = |x|+1$ | B1 B1 | soi from correctly-shaped graphs (without intercepts); but must indicate which is which; bod gf if negative $x$ values are missing |
| Graph of $|x+1|$ only | B1 | 'V' shape with $(-1,0)$ and $(0,1)$ labelled |
| Graph of $|x|+1$ | B1 [4] | 'V' shape with $(0,1)$ labelled |
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2 Given that $\mathrm { f } ( x ) = | x |$ and $\mathrm { g } ( x ) = x + 1$, sketch the graphs of the composite functions $y = \mathrm { fg } ( x )$ and $y = \operatorname { gf } ( x )$, indicating clearly which is which.
\hfill \mbox{\textit{OCR MEI C3 2010 Q2 [4]}}