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Figure 1 shows a sketch of the curve with equation $y = f(x)$, $x > 0$, where $f$ is an increasing function of $x$ - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 8
Question 3
Figure 1 shows a sketch of the curve with equation $y = f(x)$, $x > 0$, where $f$ is an increasing function of $x$. The curve crosses the $x$-axis at the point $(1, ... show full transcript
Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation $y = f(x)$, $x > 0$, where $f$ is an increasing function of $x$ - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 8
Step 1
Sketch the curve with equation $y = f(2x)$, $x > 0$
Answer
The function indicates a horizontal compression of the function by a factor of 2. This means the graph will maintain its shape but will cross the -axis at half the original point for . So, it crosses the -axis at . The general shape will be an increasing curve that approaches the -axis asymptotically and rises after crossing the -axis.
Step 2
Sketch the curve with equation $y = |f(x)|$, $x > 0$
Answer
The absolute value function negates any negative values of . As crosses the -axis at , the graph will have a cusp at this point, reflecting any negative portion of the curve upwards above the -axis. Thus, it will intersect the -axis only at and continue increasing positively from there.