The graph shows the function \(f(x)\), for \(-4 \le x \le 5\).
[VISUALIZATION: A curve starting at approximately \((-4, 1)\), decreasing to a local minimum near \((-2.5, -1)\), increasing to a local maximum near \((0, 3)\), decreasing to a local minimum near \((3, -2)\), and increasing to the endpoint \((5, 2)\). The x and y axes are shown with appropriate scales.]
(a) Write down the value of \(f(0)\). [1]
(b) Write down the interval(s) where \(f(x)\) is increasing. [2]
(c) Write down the range of \(f(x)\). [2]
(d) Find the value(s) of \(x\) for which \(f(x) = -1\). [1]
Question
Write down the value of \(f(0)\). [1]
Hint
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Look at the graph at \(x=0\) to read the corresponding y-value.
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\(f(0) = 3\)
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Write down the interval(s) where \(f(x)\) is increasing. [2]
Hint
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Identify the portions of the graph where the function is rising.
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The function is increasing on \(-2.5 < x < 0\) and \(3 < x < 5\).
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Write down the range of \(f(x)\). [2]
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Determine the minimum and maximum values shown on the graph.
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The range of \(f(x)\) is \(-2 \le f(x) \le 3\).
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Find the value(s) of \(x\) for which \(f(x) = -1\). [1]
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Look for the point(s) on the graph where the y-value is -1.
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\(x = -2.5\)
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