1. **Problem statement:** We want to find the function term of a cubic polynomial $f(x)$ that models the curve profile of a swing lounger. The function is a cubic polynomial symmetric about the origin (odd function), so it has the form: $$f(x) = ax^3 + bx^2 + cx + d$$ Since the function is symmetric about the origin (punktsymmetrisch), it must be an odd function, which means: $$f(-x) = -f(x)$$ This implies that the function contains only odd powers of $x$ and no constant term or even powers. Therefore: $$f(x) = ax^3 + cx$$ 2. **Given points:** The curve passes through the points $(-0.6, 0.1)$ and $(0.7, 0.8)$. 3. **Set up equations using the points:** For $x = -0.6$: $$f(-0.6) = a(-0.6)^3 + c(-0.6) = 0.1$$ Calculate powers: $$-0.6^3 = -0.216$$ So: $$-0.216a - 0.6c = 0.1$$ For $x = 0.7$: $$f(0.7) = a(0.7)^3 + c(0.7) = 0.8$$ Calculate powers: $$0.7^3 = 0.343$$ So: $$0.343a + 0.7c = 0.8$$ 4. **Solve the system of linear equations:** $$\begin{cases} -0.216a - 0.6c = 0.1 \\ 0.343a + 0.7c = 0.8 \end{cases}$$ Multiply the first equation by $7$ and the second by $6$ to align $c$ coefficients: $$\begin{cases} -1.512a - 4.2c = 0.7 \\ 2.058a + 4.2c = 4.8 \end{cases}$$ Add the two equations to eliminate $c$: $$(-1.512a + 2.058a) + (-4.2c + 4.2c) = 0.7 + 4.8$$ $$0.546a = 5.5$$ Solve for $a$: $$a = \frac{5.5}{0.546} \approx 10.07$$ Substitute $a$ back into the second original equation: $$0.343 \times 10.07 + 0.7c = 0.8$$ Calculate: $$3.453 + 0.7c = 0.8$$ $$0.7c = 0.8 - 3.453 = -2.653$$ $$c = \frac{-2.653}{0.7} \approx -3.79$$ 5. **Final function term:** $$f(x) = 10.07x^3 - 3.79x$$ This cubic polynomial is symmetric about the origin and fits the given points, modeling the swing lounger profile. **Answer:** $$\boxed{f(x) = 10.07x^3 - 3.79x}$$