Horizontal stretch y = f(ax)

Questions asking to sketch y = f(ax) where a is a constant inside the function argument, involving horizontal stretches or compressions of the given curve.

2 questions · Moderate -0.2

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Edexcel C1 Q8
10 marks Moderate -0.8
$$f(x) = 2x^2 + 3x - 2.$$
  1. Solve the equation \(f(x) = 0\). [2]
  2. Sketch the curve with equation \(y = f(x)\), showing the coordinates of any points of intersection with the coordinate axes. [2]
  3. Find the coordinates of the points where the curve with equation \(y = f(\frac{1}{2}x)\) crosses the coordinate axes. [3]
When the graph of \(y = f(x)\) is translated by 1 unit in the positive \(x\)-direction it maps onto the graph with equation \(y = ax^2 + bx + c\), where \(a\), \(b\) and \(c\) are constants.
  1. Find the values of \(a\), \(b\) and \(c\). [3]
AQA Paper 1 2024 June Q11
5 marks Standard +0.3
It is given that $$f(x) = x(x - a)(x - 6)$$ where \(0 < a < 6\)
  1. Sketch the graph of \(y = f(x)\) on the axes below. [3 marks] \includegraphics{figure_11a}
  2. Sketch the graph of \(y = f(-2x)\) on the axes below. [2 marks] \includegraphics{figure_11b}