The diagram shows the graphs with equations $y = f(x)$ and $y = kf(x) + a$ - Scottish Highers Maths - Question 10 - 2019
Question 10
The diagram shows the graphs with equations $y = f(x)$ and $y = kf(x) + a$.
(a) State the value of $a$.
(b) Find the value of $k$.
Worked Solution & Example Answer:The diagram shows the graphs with equations $y = f(x)$ and $y = kf(x) + a$ - Scottish Highers Maths - Question 10 - 2019
Step 1
State the value of a.
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Answer
To find the value of a, observe the vertical shift of the graph of y=kf(x)+a. The graph intersects the y-axis at the point (0, 3). Therefore, the value of a is 3.
Step 2
Find the value of k.
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Answer
To determine the value of k, we need to analyze the y-coordinates at a common point between both graphs. At x=2, the graphs meet at (2, 5). The original function f(2)=−2. Using the transformation, we have:
5=k(−2)+3
Solving this yields:
5−3=−2k2=−2kk=−1
Thus, the value of k is -1.
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