Piecewise Function 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 for x < 0; 2 * x + 1 for x >= 0
Graphing Calculator
Smallest sampled value
0.0625
Largest sampled value
25
y-intercept
1
Samples inside the domain
41
SVG path for the curve
M 0 0 L 16 39.098 L 32 76.19 L 48 111.278 L 64 144.361 L 80 175.439 L 96 204.511 L 112 231.579 L 128 256.642 L 144 279.699 L 160 300.752 L 176 319.799 L 192 336.842 L 208 351.88 L 224 364.912 L 240 375.94 L 256 384.962 L 272 391.98 L 288 396.992 L 304 400 L 320 384.962 L 336 376.942 L 352 368.922 L 368 360.902 L 384 352.882 L 400 344.862 L 416 336.842 L 432 328.822 L 448 320.802 L 464 312.782 L 480 304.762 L 496 296.742 L 512 288.722 L 528 280.702 L 544 272.682 L 560 264.662 L 576 256.642 L 592 248.622 L 608 240.602 L 624 232.581 L 640 224.561
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 for x < 0; 2 * x + 1 for x >= 0
  2. Sampled 41 points on [-5, 5] at x_i = -5 + 10 * i / 40.
  3. Sampled range: 0.0625 to 25 over 41 of 41 points.
  4. No sign change or exact zero was found on the sampled grid.
Sampled pointstable
xy
-525
-4.7522.5625
-4.520.25
-4.2518.0625
-416
-3.7514.0625
-3.512.25
-3.2510.5625
-39
-2.757.5625
-2.56.25
-2.255.0625
-24
-1.753.0625
-1.52.25
-1.251.5625
-11
-0.750.5625
-0.50.25
-0.250.0625
01
0.251.5
0.52
0.752.5
13
1.253.5
1.54
1.754.5
25
2.255.5
2.56
2.756.5
37
3.257.5
3.58
3.758.5
49
4.259.5
4.510
4.7510.5
511

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