The graph of $y = f(x)$ is shown below.
[Imagine a graph here: A smooth curve that starts in the third quadrant, increases to a local maximum in the second quadrant at approximately $x = -2$, decreases to a local minimum in the first quadrant at approximately $x = 2$, and then increases again in the first quadrant. The curve is asymptotic to $y = 1$ as $x$ approaches both positive and negative infinity. The y-intercept is at $(0,0)$.]
On the same axes, sketch the graph of a function $g(x)$ such that $g’(x) = f(x) - 1$. Clearly indicate any key features of $g(x)$, including stationary points, intervals of increase/decrease, concavity, and asymptotic behavior. Justify your reasoning.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 7 marks, testing your understanding of Derivative and Anti-derivative Graphs. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
deducing the graph of the derivative function from the graph of a given function and deducing the graph of an anti-derivative function from the graph of a given function
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