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In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y , for each unique input, x . If a vertical line intersects a curve on an xy -plane more than once then for one value of x the curve has more than one value of y , and so, the curve does not ...
Test of vertical wavy line with specified dimensions. Converted from the following vector PostScript source code: <pre>%! 10 setlinewidth 20 0 moveto 0 30 -10 45 -10 ...
For example, to multiply 5.8 by 2.13, the process is the same as to multiply 58 by 213 as described in the preceding section. To find the position of the decimal point in the final answer, one can draw a vertical line from the decimal point in 5.8, and a horizontal line from the decimal point in 2.13. (See picture for Step 4.)
Variations of the horizontal line test can be used to determine whether a function is surjective or bijective: The function f is surjective (i.e., onto) if and only if its graph intersects any horizontal line at least once. f is bijective if and only if any horizontal line will intersect the graph exactly once.
In the two-dimensional case, first, represent line i as a point p i on the line and a unit normal vector n̂ i, perpendicular to that line. That is, if x 1 and x 2 are points on line 1, then let p 1 = x 1 and let ^:= [] ‖ ‖ which is the unit vector along the line, rotated by a right angle.
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.