Graphing Calculator

y = f(x), or z = f(x, y) in 3D mode. In piecewise mode separate the branches with "|".
A second curve g(x). Its intersections with f(x) are reported.
Ignored in 3D mode, which always uses x and y.
Points on the x grid, endpoints included.
Ascending cut points. Each branch applies from its breakpoint up to the next one.
In parametric mode the "Function" field is x(t) and this one is y(t).
Function plotted
x^2 - 4
Graphing Calculator
Smallest sampled value
-4
Largest sampled value
96
y-intercept
-4
Samples inside the domain
21
SVG path for the curve
M 0 0 L 32 76 L 64 144 L 96 204 L 128 256 L 160 300 L 192 336 L 224 364 L 256 384 L 288 396 L 320 400 L 352 396 L 384 384 L 416 364 L 448 336 L 480 300 L 512 256 L 544 204 L 576 144 L 608 76 L 640 0
Worked out from OpenStax College Algebra 2e, section 3.2 Domain and Range and 3 other sources.

How this is worked out

4 steps
  1. f(x) = x^2 - 4
  2. Sampled 21 points on [-10, 10] at x_i = -10 + 20 * i / 20.
  3. Sampled range: -4 to 96 over 21 of 21 points.
  4. Zeros in the interval: -2, 2 (exact grid zeros plus bisected sign changes).
Zeros in the intervaltable
-2, 2
Sampled pointstable
xy
-1096
-977
-860
-745
-632
-521
-412
-35
-20
-1-3
0-4
1-3
20
35
412
521
632
745
860
977
1096

Results are general information, not financial, tax, legal, medical or engineering advice.