How does the range of a function relate to its graph?

Answer 1

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^2# 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)

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Answer 2

The range of a function corresponds to the set of all possible output values produced by the function. In terms of its graph, the range represents the vertical extent of the graph, indicating the lowest and highest points that the function reaches along the y-axis. Essentially, the range of a function is directly connected to the vertical span of its graph.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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