Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

) Find f(−5), f(−1), f(0), f(1), f(3), and f(5) for y = f(x) 

**Graph Analysis** The provided graph features a Cartesian coordinate system with both \(x\)- and \(y\)-axes ranging from \(-5\) to \(5\). The axes intersect at the origin (0,0). The graph includes a curve and several notable data points plotted along this curve. ### Key Graph Features: 1. **Curve Behavior**: - The curve starts at the point \((-5, 4)\). - It dips down to a local minimum at \((-4, -1.5)\). - It then rises to a local maximum at \((-1, 2)\). - After reaching this peak, the curve dips again to a value of \( (0, 0)\). - The curve rises again, reaching a point at \( (2, 2)\). - The curve then decreases steadily to a point at \( (3, 2)\). - Finally, the curve sharply drops to the point \((5,0)\). 2. **Data Points**: - Solid black filled: These points occur at \((-5, 4)\), \((-4, -1.5)\), \((0, -3)\). - Unfilled (White): These points occur at \((-1, 2)\), \((1, 1)\), \((2, 2)\), \((3, 2)\), \((4, 4)\) and `5, ### Points of Interest: - \((-5,4)\) - \((-4,-1.5)\) - \((-1, 2)\) (Open point) - \((0,0)\) - \((2,2)\) (Open point) - \((3,2)\) (Open point) - \((5,0)\) (Solid point) ### Observations: 1. The graph displays both filled and unfilled points (indicating inclusive and exclusive bounds, respectively). 2. The curve has multiple peaks and troughs, indicating the graph includes local maxima and minima throughout the interval from \(-5\) to \(5\). This type of graph is typically used in calculus to illustrate concepts of continuity, limits, and extremum points. It is important to note these characteristics when analyzing the curve to understand its overall behavior and implications in the function it represents.
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Transcribed Image Text:**Graph Analysis** The provided graph features a Cartesian coordinate system with both \(x\)- and \(y\)-axes ranging from \(-5\) to \(5\). The axes intersect at the origin (0,0). The graph includes a curve and several notable data points plotted along this curve. ### Key Graph Features: 1. **Curve Behavior**: - The curve starts at the point \((-5, 4)\). - It dips down to a local minimum at \((-4, -1.5)\). - It then rises to a local maximum at \((-1, 2)\). - After reaching this peak, the curve dips again to a value of \( (0, 0)\). - The curve rises again, reaching a point at \( (2, 2)\). - The curve then decreases steadily to a point at \( (3, 2)\). - Finally, the curve sharply drops to the point \((5,0)\). 2. **Data Points**: - Solid black filled: These points occur at \((-5, 4)\), \((-4, -1.5)\), \((0, -3)\). - Unfilled (White): These points occur at \((-1, 2)\), \((1, 1)\), \((2, 2)\), \((3, 2)\), \((4, 4)\) and `5, ### Points of Interest: - \((-5,4)\) - \((-4,-1.5)\) - \((-1, 2)\) (Open point) - \((0,0)\) - \((2,2)\) (Open point) - \((3,2)\) (Open point) - \((5,0)\) (Solid point) ### Observations: 1. The graph displays both filled and unfilled points (indicating inclusive and exclusive bounds, respectively). 2. The curve has multiple peaks and troughs, indicating the graph includes local maxima and minima throughout the interval from \(-5\) to \(5\). This type of graph is typically used in calculus to illustrate concepts of continuity, limits, and extremum points. It is important to note these characteristics when analyzing the curve to understand its overall behavior and implications in the function it represents.
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