Range
Key Questions
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The range of a function is the set of all possible outputs of that function.
For example, let's look at the function
y = 2xy=2x Since we can plug in any x value and multiple it by 2, and since any number can be divided by 2, the output of the function, the
yy values, can be any real number.Therefore, the range of this function is "all real numbers"
Let's look at something slightly more complicated, a quadratic in vertex form:
y=(x-3)^2+4y=(x−3)2+4 . This parabola has a vertex at(3,4)(3,4) and opens upwards, therefore the vertex is the minimum value of the function. The function never goes below 4, therefore the range isy>=4y≥4 .
Shreyans Bhansali
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Jul 23 2014
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Wataru
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Nov 2 2014
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The range of a function is its y-values or outputs. If you look at the graph from lowest point to highest point, that will be the range.
Ex:
y = x^2y=x2 has a range of y>=≥ 0 since the vertex is the lowest point, and it lies at (0,0).
Ex: y = 2x + 1 has a range from
-\infty−∞ to\infty∞ since the ends of the graph point in those directions. (down and left, and up and right)
In interval notation, you would write(-\infty,\infty)(−∞,∞) .Ex: Some functions have interesting ranges like the sine function.
y = sin(x)
Its highest values are 1 and its lowest values are -1. That range is-1<=y<=1−1≤y≤1 or [-1,1] in interval notation.Ex: A rather complicated function with a very challenging range is the inverse or reciprocal function,
y=frac{1}{x}y=1x .The output values might be difficult to describe except to say that they seem to include all real numbers except 0. (there is a horizontal asymptote on the x-axis)
You could write
(-\infty,0)U(0,\infty)(−∞,0)U(0,∞) in interval notation.Enjoy your study of range!
MrsRudolph221
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Sep 10 2014