DP Mathematics SL Questionbank

• Syllabus

2.3

Sub sections and their related questions

Transformations of graphs.

• 12N.2.sl.TZ0.9a: Sketch the graph of f , for \( - 1 \le x \le 5\) .
• 12N.2.sl.TZ0.9b: This function can also be written as \(f(x) = {(x - p)^2} - 3\) . Write down the value of p .
• 12N.2.sl.TZ0.9c: The graph of g is obtained by reflecting the graph of f in the x-axis, followed by a translation...
• 12N.2.sl.TZ0.9d: The graph of g is obtained by reflecting the graph of f in the x-axis, followed by a translation...
• 12N.2.sl.TZ0.9e: The graph of \(g\) is obtained by reflecting the graph of \(f\) in the x-axis, followed by a...
• 12M.1.sl.TZ2.5a: Sketch the graph of \(f( - x)\) on the grid below.
• 12M.1.sl.TZ2.5b: The graph of f is transformed to obtain the graph of g . The graph of g is shown below. The...
• 08N.1.sl.TZ0.10b: The transformation P is given by a horizontal stretch of a scale factor of \(\frac{1}{2}\) ,...
• 08N.1.sl.TZ0.10c: The graph of g is the image of the graph of f under P. Find \(g(t)\) in the form...
• 08N.1.sl.TZ0.10d: The graph of g is the image of the graph of f under P. Give a full geometric description of the...
• 08M.1.sl.TZ1.9d: Let \(g(x) = {x^2}\) . The graph of f may be obtained from the graph of g by the two...
• 08M.1.sl.TZ2.5a: On the same diagram sketch the graph of \(y = - f(x)\) .
• 08M.1.sl.TZ2.5b(i) and (ii): Let \(g(x) = f(x + 3)\) . (i)     Find \(g( - 3)\) . (ii)    Describe fully the transformation...
• 10N.1.sl.TZ0.9a: Find \((f \circ g)(x)\) .
• 10N.1.sl.TZ0.9b: The vector \(\left( {\begin{array}{*{20}{c}}3\\{ - 1}\end{array}} \right)\) translates the graph...
• 10N.1.sl.TZ0.9c: The vector \(\left( {\begin{array}{*{20}{c}}3\\{ - 1}\end{array}} \right)\) translates the graph...
• 10N.1.sl.TZ0.9d: The vector \(\left( {\begin{array}{*{20}{c}}3\\{ - 1}\end{array}} \right)\) translates the graph...
• 10M.1.sl.TZ1.8a: Find the coordinates of A.
• 10M.1.sl.TZ1.8b(i), (ii) and (iii): Write down the coordinates of (i)     the image of B after reflection in the y-axis; (ii)   ...
• 09N.1.sl.TZ0.4a: Let \(h(x) = f( - x)\) . Sketch the graph of \(h\) on the grid below.
• 09N.1.sl.TZ0.4b: Let \(g(x) = \frac{1}{2}f(x - 1)\) . The point \({\text{A}}(3{\text{, }}2)\) on the graph of...
• 09M.1.sl.TZ1.5a: The graph of g can be obtained from the graph of f using two transformations. Give a full...
• 09M.1.sl.TZ1.5b: The graph of g is translated by the...
• 09M.1.sl.TZ1.10a: Show that \(f( - x) = - f(x)\) .
• 09M.2.sl.TZ2.2a: On the same grid sketch the graph of \(y = f( - x)\) .
• 09M.2.sl.TZ2.2b: Complete the following table.
• 09M.2.sl.TZ2.2c: Give a full geometric description of the transformation that gives the image in Diagram A.
• SPNone.1.sl.TZ0.8d: Let \(g(x) = {x^2}\) . The graph of f may be obtained from the graph of g by the following two...
• 11N.2.sl.TZ0.7a: Find \(v(t)\) , giving your answer in the form \(a{(t - b)^2} + c\) .
• 11N.2.sl.TZ0.7b: A particle moves along a straight line so that its velocity in ms−1 , at time t seconds, is given...
• 11M.2.sl.TZ1.2a: Write down the coordinates of the vertex of the graph of g .
• 11M.2.sl.TZ1.2b: Express g in the form \(g(x) = 3{(x - p)^2} + q\) .
• 11M.2.sl.TZ1.2c: The graph of h is the reflection of the graph of g in the x-axis. Write down the coordinates of...
• 11M.1.sl.TZ2.5a: Express \(g(x)\) in the form \(f(x) + \ln a\) , where \(a \in {{\mathbb{Z}}^ + }\) .
• 11M.1.sl.TZ2.5b: The graph of g is a transformation of the graph of f . Give a full geometric description of this...
• 14M.1.sl.TZ2.8e: The graph of \(f\) has its vertex on the \(x\)-axis. The graph of a function \(g\) is obtained...
• 13M.2.sl.TZ1.6a: The graph of \(f\) is mapped to the graph of \(g\) under the following transformations: vertical...
• 13M.2.sl.TZ1.6b: Let \(h(x) = - g(3x)\) . The point A(\(6\), \(5\)) on the graph of \(g\) is mapped to the point...
• 15M.1.sl.TZ1.4c: On the same diagram, sketch the graph of \(y = f( - x)\).
• 15N.1.sl.TZ0.8c: Let \(g(x) =  - {(x - 3)^2} + 1\). The graph of \(g\) is obtained by a reflection of the graph of...
• 16M.1.sl.TZ1.9a: Find the \(x\)-coordinate of P.
• 16M.1.sl.TZ1.9b: Find \(f(x)\), expressing your answer as a single logarithm.
• 16M.1.sl.TZ1.9c: The graph of \(f\) is transformed by a vertical stretch with scale factor \(\frac{1}{{\ln 3}}\)....
• 17M.2.sl.TZ1.10a.i: Write down the value of \(q\);
• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...

Translations: \(y = f\left( x \right) + b\) ; \(y = f(x - a)\) .

• 14M.1.sl.TZ2.8e: The graph of \(f\) has its vertex on the \(x\)-axis. The graph of a function \(g\) is obtained...
• 15M.2.sl.TZ1.7b: The graph of \(f\) is translated to the graph of \(g\) by the vector...
• 15M.2.sl.TZ2.5b: The graph of \(f\) is translated by the vector...
• 15N.1.sl.TZ0.8c: Let \(g(x) =  - {(x - 3)^2} + 1\). The graph of \(g\) is obtained by a reflection of the graph of...
• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...

Reflections (in both axes): \(y = - f\left( x \right)\) ; \(y = f( - x)\) .

• 14M.1.sl.TZ2.8e: The graph of \(f\) has its vertex on the \(x\)-axis. The graph of a function \(g\) is obtained...
• 15M.1.sl.TZ1.4c: On the same diagram, sketch the graph of \(y = f( - x)\).
• 15N.1.sl.TZ0.8c: Let \(g(x) =  - {(x - 3)^2} + 1\). The graph of \(g\) is obtained by a reflection of the graph of...
• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...

Vertical stretch with scale factor \(p\): \(y = pf\left( x \right)\) .

• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...

Stretch in the x-direction with scale factor \(\frac{1}{q}\): \(y = f(qx)\) .

• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...

Composite transformations.

• 09N.1.sl.TZ0.4b: Let \(g(x) = \frac{1}{2}f(x - 1)\) . The point \({\text{A}}(3{\text{, }}2)\) on the graph of...
• 09M.1.sl.TZ1.5a: The graph of g can be obtained from the graph of f using two transformations. Give a full...
• 09M.1.sl.TZ1.5b: The graph of g is translated by the...
• 09M.1.sl.TZ1.10c: It is given that \(\int {f(x){\rm{d}}x = \frac{a}{2}} \ln ({x^2} + 1) + C\) . (i)     Find the...
• SPNone.1.sl.TZ0.8d: Let \(g(x) = {x^2}\) . The graph of f may be obtained from the graph of g by the following two...
• 13M.2.sl.TZ1.6a: The graph of \(f\) is mapped to the graph of \(g\) under the following transformations: vertical...
• 13M.2.sl.TZ1.6b: Let \(h(x) = - g(3x)\) . The point A(\(6\), \(5\)) on the graph of \(g\) is mapped to the point...
• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...