Moderate -0.8 This question requires understanding of composite functions and modulus graphs, but involves straightforward application of standard transformations. Students need to recognize that fg(x) = |x+1| (horizontal shift) and gf(x) = |x|+1 (vertical shift), then sketch these basic V-shaped graphs with clearly labeled vertices. The conceptual demand is low and the sketching is routine for C3 level.
6 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 6:
| $fg(x) = |x+1|$ | B1 | soi from correctly-shaped graphs (i.e. without intercepts); but must indicate which is which |
|---|---|---|
| $gf(x) = |x|+1$ | B1 | 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 | 'V' shape with $(0,1)$ labelled $(0,1)$ |
| **[4]** | | |
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6 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 Q6 [4]}}