randRangeNonZero(-3, 3)
randRangeNonZero(-5, 5)
coefficient(M) + "x"
coefficient(B) + "x"
fractionVariable(1, M, "x")
fractionVariable(-1, M, "x")
M < 0 ? "-\\dfrac{" + (-M) + "}{x}" : "\\dfrac{" + M + "}{x}"
fractionVariable(1, M, "y")
fractionReduce(B, M)
fractionReduce(M, B)
function( x ) { return M * x + B; }
function( x ) { return ( x - B ) / M; }
[
[X_OVER_M, "-", B_OVER_M],
[M_X, "-", B],
[M_X, "+", B],
[B_X, "+", M],
[M_OVER_X, "+", B],
[X_OVER_M, "+", B],
[X_OVER_M, "-", B],
[X_OVER_M, "-", M_OVER_B],
[X_OVER_M, "+", B_OVER_M],
[X_OVER_NEG_M, "-", B_OVER_M],
[X_OVER_NEG_M, "+", B_OVER_M]
]
sanitizeChoices(CHOICES_RAW)
Consider f given by f(x) = M_X + B.
graphInit({
range: 10.8,
scale: 20,
tickStep: 1,
labelStep: 2,
})
label( [ 0, 10 ], "{f(x)}", "right" );
label( [ 10, 0 ], "x", "above" );
// draw the function
style({
stroke: BLUE,
strokeWidth: 2
}, function() {
plot( F, [ -11, 11 ] );
});
Find f^{-1}(x) = \ldots
CHOICES[0][0]
CHOICES[0][1]
CHOICES[0][2]
-
CHOICE[0]
CHOICE[1]
CHOICE[2]
Start with y = f(x) and solve it for x. This yields to y \mapsto x=f^{-1}(y).
\implies Y_OVER_M - B_OVER_M = x
\implies x = Y_OVER_M - B_OVER_M.
We know that f^{-1}(y) = Y_OVER_M - B_OVER_M.
var pos = function( n ) {
if ( n >= 1 ) {
return "below right";
} else if ( n > 0 ) {
return "below";
} else if ( n > -1 ) {
return "above";
} else {
return "above right";
}
},
fPos = pos( M ),
fInvPos = pos( 1 / M );
// plot function inverse
style({
stroke: RED,
strokeWidth: 2
}, function() {
plot( F_INV, [ -11, 11 ] );
});
if ( M !== -1 && ( M !== 1 || B !== 0 ) ) {
// label f
style({
color: BLUE,
strokeWidth: 1
}, function() {
label( labelPos( F ), "f", fPos );
});
// label f_inv
style({
color: RED,
strokeWidth: 1
}, function() {
label( labelPos( F_INV ), "f^{-1}", fInvPos );
});
// Show line of symmetry
style({
stroke: "#aaa",
strokeWidth: 2,
strokeDasharray: "- "
}, function() {
plot( function( x ) { return x; }, [ -11, 11 ] );
});
}
Rewritting from
y to x gives: f^{-1}(x) = X_OVER_M - B_OVER_M.
Note that the graph of f^{-1} is mirroring the graph of f w.r.t. the line y = x.