Rectangular axes plot

Using rectangular axes, we can see that the graph of y = x1/2 is half of a parabola on its side (i.e. that parabola's axis is vertical):

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Graph of `y=sqrt(x)` on linear axes.

We've seen this curve before, in The Parabola section.

Note 1: The detail near `(0, 0)` is not so good using a rectangular grid.

Note 2: The curve passes through `(0, 0)`, `(1, 1)`, `(4, 2)` and `(9, 3)`. In each case, the y-value is the square root of the x-value, which is to be expected.

Let's now see the curve using semi-logarithmic plots.

Logarithmic vertical axis, linear horizontal axis

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Graph of `y=sqrt(x)` on semilogarithmic (log-lin) axes.

Now we have a lot better detail for small y. The lowest value of y that the graph indicates is `y = 0.1`. We can go lower than this, but cannot show `y = 0`, since the logarithm of `0` is not defined.

We can see that the curve still passes through `(1, 1)`, `(4, 2)` and `(9, 3)`.

Linear vertical axis, logarithmic horizontal axis

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Points along the curve `y=sqrt(x)` using lin-log axes.

Logarithmic vertical axis, logarithmic horizontal axis (log-log) plot

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Points along the curve `y=sqrt(x)` on log-log axes.

We observe that the graph of y = x1/2 is a straight line when graphed on log-log axes.

Once again our curve passes through `(1, 1)`, `(4, 2)` and `(9, 3)` (indicated by dots on the graph), as it should.