### 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

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

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.