# Exam-Style Question on Graph Transformations

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 718. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is not allowed.

Part of the graph of a function, $$f$$ , is shown in the following diagram. The graph of $$y = f(x)$$ has a y-intercept at $$(0, 1.5)$$ , an x-intercept at $$(a , 0)$$ and horizontal asymptotes $$y = 5$$ and $$y = -2$$.

Consider the function $$g(x) = |f(|x|)|$$

(a) Sketch the graph of $$y = g(x)$$, labelling any axis intercepts and giving the equation of the asymptotes.

(b) Find the possible values of $$k$$ such that $$(g(x))^2 = k$$ has exactly four solutions.

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The screenshots used on this page were created in Desmos. If you would like to interact with the graph mentioned in this question you will find it waiting for you on the Graph Plotter.

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