sketch the graphs of the following functions: y = x, y = x2, y = x3, y = |x|, y = sqrt(x), y = 1/x, y = 1/x2, y = sqrt(a2 - x2)
Question
sketch the graphs of the following functions: y = x, y = x2, y = x3, y = |x|, y = sqrt(x), y = 1/x, y = 1/x2, y = sqrt(a2 - x2)
Solution
I'm sorry, but as a text-based AI, I'm unable to sketch or draw graphs. However, I can describe how the graphs of these functions would look:
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y = x: This is a straight line passing through the origin (0,0) with a slope of 1. It increases as x increases and decreases as x decreases.
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y = x^2: This is a parabola opening upwards with its vertex at the origin (0,0). It is symmetric about the y-axis.
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y = x^3: This graph also passes through the origin (0,0) and is symmetric with respect to the origin. It increases as x increases and decreases as x decreases, but at a faster rate than y = x.
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y = |x|: This is a V-shaped graph with its vertex at the origin (0,0). It increases as x increases and also increases as x decreases.
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y = sqrt(x): This graph starts from the origin (0,0) and increases as x increases. It is undefined for x < 0.
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y = 1/x: This graph has two parts, one in the first quadrant and one in the third quadrant. It approaches but never reaches the x-axis or y-axis.
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y = 1/x^2: This graph also has two parts in the first and second quadrants. It approaches but never reaches the x-axis, and is undefined at x = 0.
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y = sqrt(a^2 - x^2): This graph is a semi-circle with radius 'a' if 'a' is a constant. It is undefined for |x| > a.
Similar Questions
Graph the functions in Exercises 29-48y=\sqrt{x+4}y=|x-2|y=1+\sqrt{x-1}y=(x+1)^{2/3}y=1-x^{2/3}y=\sqrt[3]{x-1}-1y=\sqrt{9-x}y=|1-x|-1y=1-\sqrt{x}y=(x-8)^{2/3}y+4=x^{2/3}y=(x+2)^{3/2}+1y=\frac{1}{x-2}y=\frac{1}{x}-2y=\frac{1}{x}+2y=\frac{1}{x+2}y=\frac{1}{(x-1)^{2}}y=\frac{1}{x^{2}}+1y=\frac{1}{x^{2}}-1y=\frac{1}{(x+1)^{2}}
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