$f$

f(x) =

$g$

\textcolor{#000000}{g(x)}=\textcolor{#009900}{b}\cdot f(\textcolor{#3333FF}{a}\cdot (x-\textcolor{#CC0000}{c}))+\textcolor{#800080}{d}

d = 0 (slider from -5 to 5, step 0.1)
d_{color}: "\textcolor{#800080}{" + (LaTeX[abs(d)]) + "}"
b = 1 (slider from -5 to 5, step 0.1)
b_{color}: "\textcolor{#009900}{" + (LaTeX[b]) + "}"
c = 0 (slider from -5 to 5, step 0.1)
c_{color}: "\textcolor{#CC0000}{" + (LaTeX[abs(c)]) + "}"
text_{c} = If(c ≟ 0, "", If[c < 0, "+", "-"] + c_{color})
a = 1 (slider from -5 to 5, step 0.1)
a_{color}: "\textcolor{#3333FF}{" + (LaTeX[a]) + "}"
text_{d} = If(b ≟ 0, If[d ≟ 0, "0", d_{color}], If[d ≟ 0, "", If[d < 0, "-" + d_{color}, "+" + d_{color}]])
text_{a} = If(a ≟ 0, "0", If[a ≠ 1, a_{color} + (If[c ≠ 0, "·(", ""]), ""] + "x" + text_{c} + (If[a ≠ 1 ∧ c ≠ 0, ")", ""]))
text_{b} = If(b ≟ 0, text_{d}, If[b ≠ 1, If[b < 0, "(" + b_{color} + ")", b_{color}] + "·", ""] + "f(" + text_{a} + ")" + text_{d})
f(x) = sin(x)
function = Textfield(f)
g(x) = (b * f((a * (x - c)))) + d
d_1: "\textcolor{#800080}{" + (LaTeX[abs(d)]) + "}"
b_1: "\textcolor{#009900}{" + (LaTeX[b]) + "}"
c_1: "\textcolor{#CC0000}{" + (LaTeX[abs(c)]) + "}"
text_2 = If(c ≟ 0, "", If[c < 0, "+", "-"] + c_1)
a_1: "\textcolor{#3333FF}{" + (LaTeX[a]) + "}"
text_3 = If(b ≟ 0, If[d ≟ 0, "0", d_1], If[d ≟ 0, "", If[d < 0, "-" + d_1, "+" + d_1]])
text_4 = If(a ≟ 0, "0", If[a ≠ 1, a_1 + (If[c ≠ 0, "·(", ""]), ""] + "x" + text_2 + (If[a ≠ 1 ∧ c ≠ 0, ")", ""]))
text_5 = If(b ≟ 0, text_3, If[b ≠ 1, If[b < 0, "(" + b_1 + ")", b_1] + "·", ""] + "f(" + text_4 + ")" + text_3)
text: "=" + (LaTeX[text_{b}]) + ""