Mathski
Worksheet
Transforming Graphs
IB Mathematics AA · SL & HL · Shadow Worksheet
Practice
Name
Question 1
Describe the transformation that maps \(y=f(x)\) to each of the following:
(a)\(y=f(x)+4\)
(b)\(y=f(x-3)\)
(c)\(y=2f(x)\)
(d)\(y=f(2x)\)
(e)\(y=-f(x)\)
(f)\(y=f(-x)\)
(a)
Answer
Translation \(egin{pmatrix}0\4\end{pmatrix}\)
(b)
Answer
Translation \(egin{pmatrix}3\0\end{pmatrix}\)
(c)
Answer
Stretch, scale factor 2, parallel to \(y\)-axis
(d)
Answer
Stretch, scale factor \( frac{1}{2}\), parallel to \(x\)-axis
(e)
Answer
Reflection in the \(x\)-axis
(f)
Answer
Reflection in the \(y\)-axis
Question 2
The graph of \(y=x^2\) is transformed to give each graph below. Write down the equation of each:
(a)Translated 3 right and 2 up
(b)Reflected in the \(x\)-axis
(c)Stretched scale factor 3 parallel to \(y\)-axis then translated 1 left
(a)
Answer
\(y=(x-3)^2+2\)
(b)
Answer
\(y=-x^2\)
(c)
Answer
\(y=3(x+1)^2\)
Question 3
The point \((2,-3)\) lies on \(y=f(x)\). Write down the image of this point under each transformation:
(a)\(y=f(x-1)+4\)
(b)\(y=3f(x)\)
(c)\(y=f(2x)\)
(a)
Answer
\((3,\,1)\)
(b)
Answer
\((2,\,-9)\)
(c)
Answer
\((1,\,-3)\)
Question 4
Sketch \(y=|x^2-4|\), labelling all intercepts and any key points.
Base graph
\(y=x^2-4\): roots at \(x=\pm2\), vertex \((0,-4)\)
Apply modulus
Reflect portion below \(x\)-axis upward
Key features
Intercepts at \(x=\pm2\); \(y\)-int: \((0,4)\); local min at \(x=0,y=4\); local min at \(x=\pm2,y=0\)
Question 5
Given \(f(x)=\sin x\), write down the equation of the graph with amplitude 3, period \(\pi\), and translated \( frac{\pi}{4}\) to the right.
Amplitude 3: multiply by 3. Period \(\pi\): replace \(x\) with \(2x\). Shift right \( frac{\pi}{4}\): replace \(x\) with \(x- frac{\pi}{4}\)
Answer
\(y=3\sin\!\left(2\!\left(x-\dfrac{\pi}{4} ight) ight)=3\sin(2x- frac{\pi}{2})=-3\cos(2x)\)
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