Math Lab
← All labs

Function Family Mixer

Relations and Functions · Class XI

Mix linear, quadratic, modulus and reciprocal pieces with coefficient sliders to see compound shapes.

1
type a value
-33
0
type a value
-22
0
type a value
-22
0
type a value
-33
Live values
  • f(0⁺)0.001
  • f(1)1
  • f(−1)-1
xy
  • f(x) = a x + b x² + c|x| + d/x

Formulas in this lab

  • f(0⁺)
    f(0+)f(0^{+})
  • f(1)
    f(1)=a+b+c+df(1) = a + b + c + d
  • f(−1)
    f(−1)=−a+b+c−df(-1) = -a + b + c - d
Tip: Set b = c = d = 0 for a pure line; flip on b alone for a parabola.

Frequently asked questions

▶What does $f(x) = ax + bx^2 + c|x| + d/x$ mean?

It is a family of four building blocks: linear $ax$, quadratic $bx^2$, modulus $c|x|$ and reciprocal $d/x$. Turning the four weights on and off lets you see how each piece contributes to the overall shape. This previews ideas you will reuse in Class XII and JEE function questions.

▶How do I use the function family mixer lab?

Slide the four coefficients $a$, $b$, $c$, $d$. Set three to zero to isolate one piece, then mix two at a time. Try $a = 1$, $b = 0.5$, others zero, to see a parabola tilted by a linear drift. The lab also reports $f(0^+)$, $f(1)$ and $f(-1)$.

▶Even, odd or neither: how do I tell from the formula?

Even functions satisfy $f(-x) = f(x)$ (mirror in y-axis): the $bx^2$ and $c|x|$ pieces. Odd functions satisfy $f(-x) = -f(x)$ (rotational symmetry): the $ax$ and $d/x$ pieces. Mixing odd and even pieces breaks both symmetries — a common JEE trap.

▶Why are reciprocal terms a domain headache?

The $d/x$ piece blows up at $x = 0$, so the natural domain becomes $\mathbb{R}\setminus\{0\}$. Marking-scheme rubrics dock marks for forgetting to exclude $x = 0$. The lab evaluates $f(0^+)$ to make that singular behaviour visually obvious.