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Exam-Style Questions on Absolute Value GraphsProblems on Absolute Value Graphs adapted from questions set in previous Mathematics exams. |
1. | IB Analysis and Approaches |
The graph of \( y = f(|x|) \) for \( -2 \leq x \leq 2 \) is shown in the following diagram.
(a) On the following axes, sketch the graph of \( y = |f(|x|)| \) for \( -2 \leq x \leq 2 \).
It is given that \( f \) is an odd function.
(b) On the following axes, sketch the graph of \( y = f(x) \) for \( -2 \leq x \leq 2 \).
It is also given that
$$ \int_{0}^{2} f(|x|) \, dx = \dfrac{2}{3} $$(c) Write down the value of
$$ \int_{-2}^{2} f(x) \, dx; $$(d) Evaluate
$$ \int_{-2}^{2} \left( f(|x|) + f(x) \right) \, dx. $$If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
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