DP Mathematics HL Questionbank

• Syllabus

2.3

Sub sections and their related questions

Transformations of graphs: translations; stretches; reflections in the axes.

• 12M.2.hl.TZ1.6: Let \(f(x) = \ln x\) . The graph of f is transformed into the graph of the function g by a...
• 12N.1.hl.TZ0.3b: If g(x) = 3f(x − 2) , (i)     state the coordinates of the points where the graph of g...
• 11M.1.hl.TZ2.1b: The graph of f(x) is translated 3 units in the positive direction parallel to the x-axis....
• 13M.1.hl.TZ1.12b: The graph of \(y = {x^2}\) is transformed onto the graph of \(y = 4{x^2} - 4x + 5\). Describe a...
• 10M.1.hl.TZ2.2: (a)     Express the quadratic \(3{x^2} - 6x + 5\) in the form \(a{(x + b)^2} + c\), where a, b, c...
• 09M.2.hl.TZ2.4a: The graph of \(y = \ln (x)\) is transformed into the graph of \(y = \ln \left( {2x + 1} \right)\)...
• 14M.1.hl.TZ2.8b: The graph of the function \(g\) is obtained by applying the following transformations to the...
• 13N.1.hl.TZ0.10e: Sketch the graphs of \(y = f(x)\) and \(y = g(x)\) on the same axes, showing clearly the points...
• 13N.1.hl.TZ0.10d: The graph of the function \(g\) is obtained from the graph of \(f\) by stretching it in the...
• 14N.1.hl.TZ0.1a: Find an expression for \(g(x)\).
• 15M.1.hl.TZ1.9d: The graph of \(y = g \circ f(x)\) can be obtained by applying four transformations to the graph...
• 15M.2.hl.TZ2.6a: Find the value of \(a\) and the value of \(b\).
• 17M.2.hl.TZ1.5b: Find the probability that exactly seven rooms will have fewer than three faults in the carpet.

The graph of the inverse function as a reflection in \(y = x\).

• 12M.1.hl.TZ2.10b: Sketch the graph of f .
• 11M.1.hl.TZ2.13c: The increasing function f satisfies \(f(0) = 0\) and \(f(a) = b\) , where \(a > 0\) and...
• 13M.1.hl.TZ2.12d: (i)     Find an expression for \({f^{ - 1}}(x)\). (ii)     Sketch the graph of \(y = f(x)\),...
• 12M.1.hl.TZ1.4: The graph below shows \(y = f(x)\) , where \(f(x) = x + \ln x\) .   (a) On the graph below,...
• 13N.1.hl.TZ0.3a: Sketch the graph of \(y = {f^{ - 1}}(x)\) on the same axes.
• 15N.2.hl.TZ0.12b: (i)     Explain why \(f\) does not have an inverse. (ii)     The domain of \(f\) is restricted...