x2 . x +1
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EXAMPLE 20 Here are three ways to plot the graph y =
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x2 Plot x 2 + 1 , {x, 3, 3}
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x2 Plot x 2 + 1 , {x, 3, 3}, Ticks None
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x2 Plot x2 +1 , {x, 3, 3}, Ticks {{ 3, 3}, Automatic}
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Two-Dimensional Graphics
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The option Filling will plot a shaded graph.
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Filling Axis fills from the curve to the x-axis. Filling Top fills from the curve to the top of the plot. Filling Bottom fills from the curve to the bottom of the plot. Filling y fills from the curve to value y in the vertical direction. Filling {m} fills to the mth curve. Filling {m {n}} fills from the mth curve to the nth curve. Filling {m {y, g}} fills from the mth curve to the value y using style option g. Filling {m {{n}, g}} fills from the mth curve to the nth curve using style option g.
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EXAMPLE 21
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Plot[1 x2, {x, 1, 1}, Filling Axis]
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1.0 0.8 0.6 0.4 0.2
1.0
0.5
Plot[{1 x2, 2 2 x2},{x, 1, 1}, Filling {1 {2}}]
1.0
0.5
Plot[{1 x2, 2 2 x2, 3 3 x2}, {x, 1, 1}, Filling {1 {2}, 2 {3}}]
3.0 2.5 2.0 1.5 1.0 0.5 1.0 0.5 0.5 1.0
Two-Dimensional Graphics
EXAMPLE 22
Plot[{1 x2, 2 2 x2, 3 3 x2}, {x, 1, 1}, Filling {1 {0, Orange}, 1 {{2}, Green}, 2 {{3}, Yellow}}]
3.0 2.5 2.0 1.5 1.0 0.5 1.0 0.5 0.5 1.0
SOLVED PROBLEMS
4.1 Plot the graph of y = xe x from x = 0 to x = 5.
SOLUTION
Plot[x Exp[ x], {x, 0, 5}]
0.35 0.30 0.25 0.20 0.15 0.10 0.05 1 2 3 4 5
4.2 Plot f ( x ) = | 1 | x | | on the interval [ 3, 3].
SOLUTION
Plot[Abs[1 Abs[x]], {x, 3, 3}]
2.0 1.5
1.0 0.5
Two-Dimensional Graphics
4.3 The standard normal curve used in probability and statistics is defined by the function f (x) = Sketch the graph for 3 x 3.
SOLUTION
1 1 x2 e 2 2
f[x_]= 1 Exp 1 x 2 ; 2 2 Plot[f[x], {x, 3, 3}]
4.4 Plot the graphs y = sin x , y = 2 sin x , and y = 3 sin x from 2 to 2 on the same set of axes.
SOLUTION
, Plot[{Sin[x] 2 Sin[x], 3 Sin[x]}, {x, 2 o, 2 o}]
3 2 1
2 1 2 3
4.5 The graphs of inverse functions are symmetric with respect to the line y = x. Plot the inverse functions f ( x ) = x 2, 0 x 2, and f 1 ( x ) = x , 0 x 4, as solid curves and the line y = x as a dotted line and observe the symmetry.
Two-Dimensional Graphics
SOLUTION
g1 = Plot[ x 2 , {x, 0, 2}]; g2 = Plot[ x , {x, 0, 4}]; g3 = Plot[x, {x, 0, 4}, PlotStyle Dashing[{0, 0, .01}]]; Show[g1, g2, g3, AspectRatio Automatic, PlotRange {{0, 4}, Automatic}]
4.6 Sketch the graphs of y = x 2 , y = x 2, and y = x 2 sin 10 x , 2 x 2 , on a single set of axes enclosed by a frame.
SOLUTION
Plot[{x2, x2, x2 Sin[10 x]}, {x, 2 o, 2 o}, Frame True]
40 6 4 2 0 2 4 6
Two-Dimensional Graphics
4.7 The family of Chebyshev polynomials is used in approximation theory and numerical analysis. Mathematica represents these polynomials as ChebyshevT[n, x]. On a single set of axes, using some device to distinguish the curves, plot a labeled graph showing the Chebyshev polynomials of degrees 2, 3, and 4.
SOLUTION 1
PlotLegends` Plot[{ChebyshevT[2, x], ChebyshevT[3, x], ChebyshevT[4, x]}, {x, 2, 2}, PlotStyle {GrayLevel[0], GrayLevel[.4], GrayLevel[.7]}, PlotLegend {"T2", "T3", "T4"}, LegendPosition {1,0}]
T1 20 15 10 T3 5 2 1 5 10 1 2 T2
SOLUTION 2
PlotLegends` Plot[{ChebyshevT[2, x], ChebyshevT[3, x], ChebyshevT[4, x]}, {x, 2, 2}, PlotStyle {Red, Green, Blue}, PlotLegend {"T2", "T3", "T4"}, LegendPosition {1, 0}]
Color graph not shown.
Sketch the graphs of y = 1 + sin x , 0 x 2 , y = 2 + sin x , 2 x 4 , and y = 3 + sin, 4 x 6 on one set of axes.
