Figure 1 shows the sketch of a curve with equation $y = f(x)$, $x
e ext{R}$ - Edexcel - A-Level Maths Pure - Question 5 - 2018 - Paper 1
Question 5
Figure 1 shows the sketch of a curve with equation $y = f(x)$, $x
e ext{R}$.
The curve crosses the y-axis at (0, 4) and crosses the x-axis at (5, 0).
The curve h... show full transcript
Worked Solution & Example Answer:Figure 1 shows the sketch of a curve with equation $y = f(x)$, $x
e ext{R}$ - Edexcel - A-Level Maths Pure - Question 5 - 2018 - Paper 1
Step 1
State the coordinates of the turning point on the curve with equation $y = f(x - 2)$
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Answer
The coordinates of the turning point for the curve y=f(x−2) can be derived from the original turning point. The original turning point at (2,7) gets shifted by 2 units to the right. Therefore, the new coordinates will be (2+2,7)=(4,7).
Step 2
State the solution of the equation $f(2x) = 0$
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Answer
To find the solution for f(2x)=0, we need to determine the values of x for which f(x)=0. From the information provided, f(x) crosses the x-axis at x=5. Therefore, setting 2x=5 gives:
$$egin{align*}2x &= 5 \ x &= rac{5}{2} = 2.5 ext{.}\ \ ext{Hence, the solution is: }(x) = 2.5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ext{Whereas (2.5,0) is the point on the curve.}
ext{Alternatively, allow for brackets: }(x) = 2.5.
Step 3
State the equation of the asymptote to the curve with equation $y = f(-x)$
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Answer
The asymptote of the curve is defined by the line y=1. Since reversing the x-coordinates in f(−x) does not affect the asymptote, the equation remains:
y=1.
Step 4
State the set of possible values for $k.$
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Answer
Given that the line y=k meets the curve y=f(x) at only one point, the possible values for k can either be:
k<1
k=7
Thus, the complete set of possible values is expressed as:
