Single transformation sketch

Questions asking to sketch a single transformation of f(x) such as f(x+a), f(ax), af(x), or |f(x)|, showing key features like intercepts and turning points.

5 questions · Moderate -0.7

1.02w Graph transformations: simple transformations of f(x)
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AQA C3 2013 June Q6
4 marks Moderate -0.3
6
  1. Sketch the graph of \(y = \cos ^ { - 1 } x\), where \(y\) is in radians. State the coordinates of the end points of the graph.
  2. Sketch the graph of \(y = \pi - \cos ^ { - 1 } x\), where \(y\) is in radians. State the coordinates of the end points of the graph.
    (2 marks) \includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-05_759_1258_678_431} \includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-05_751_1241_1564_443}
Edexcel C3 Q3
9 marks Standard +0.3
The function f is even and has domain \(\mathbb{R}\). For \(x \geq 0\), f(x) = \(x^2 - 4ax\), where \(a\) is a positive constant.
  1. In the space below, sketch the curve with equation \(y = \text{f}(x)\), showing the coordinates of all the points at which the curve meets the axes. [3]
  2. Find, in terms of \(a\), the value of f(2a) and the value of f(-2a). [2]
Given that \(a = 3\),
  1. use algebra to find the values of \(x\) for which f(x) = 45. [4]
WJEC Unit 1 2023 June Q11
7 marks Moderate -0.8
The function \(f\) is defined by \(f(x) = \frac{8}{x^2}\).
  1. Sketch the graph of \(y = f(x)\). [2]
  2. On a separate set of axes, sketch the graph of \(y = f(x - 2)\). Indicate the vertical asymptote and the point where the curve crosses the \(y\)-axis. [3]
  3. Sketch the graphs of \(y = \frac{8}{x}\) and \(y = \frac{8}{(x-2)^2}\) on the same set of axes. Hence state the number of roots of the equation \(\frac{8}{(x-2)^2} = \frac{8}{x}\). [2]
WJEC Unit 1 Specimen Q7
5 marks Moderate -0.8
Figure 1 shows a sketch of the graph of \(y = f(x)\). The graph has a minimum point at \((-3, -4)\) and intersects the \(x\)-axis at the points \((-8, 0)\) and \((2, 0)\). \includegraphics{figure_1}
  1. Sketch the graph of \(y = f(x + 3)\), indicating the coordinates of the stationary point and the coordinates of the points of intersection of the graph with the \(x\)-axis. [3]
  2. Figure 2 shows a sketch of the graph having one of the following equations with an appropriate value of either \(p\), \(q\) or \(r\). \(y = f(px)\), where \(p\) is a constant \(y = f(x) + q\), where \(q\) is a constant \(y = rf(x)\), where \(r\) is a constant \includegraphics{figure_2} Write down the equation of the graph sketched in Figure 2, together with the value of the corresponding constant. [2]
OCR AS Pure 2017 Specimen Q1
5 marks Easy -1.8
The diagram below shows the graph of \(y = f(x)\). \includegraphics{figure_1}
  1. On the diagram in the Printed Answer Booklet draw the graph of \(y = f(x + 3)\). [2]
  2. Describe fully the transformation which transforms the graph of \(y = f(x)\) to the graph of \(y = -f(x)\). [1]
The point \((2, 3)\) lies on the graph of \(y = g(x)\). State the coordinates of its image when \(y = g(x)\) is transformed to
  1. \(y = 4g(x)\) [1]
  2. \(y = g(4x)\). [1]