B2. Graphically determine the intersection of the graphs of functions $f$ and $g$ with the rules $f(x)=3^{x}-1$ and $g(x)=x^{2}-2 x$. Verify the solution by calculation.
B2. We draw the asymptote $y=-1$, the intersection $z$ with the ordinate $(0,0)$, and calculate an additional point, for example, $(1,2)$, and then draw the graph of the exponential function. For the quadratic function, we calculate the roots $x_{1}=0$ and $x_{2}=2$ and the vertex $(1,1)$, and then draw its graph. We read off the intersection $(0,0)$. We verify the solution computationally: $f(0)=3^{0}-1=1-1=0$ and $g(0)=0^{2}-2 \cdot 0=0$.

Drawn asymptote $y=1$

1 point

Drawn intersection $z$ with the ordinate $(0,0)$ 1 point

Calculated and drawn roots of the quadratic function $x_{1}=0$ and $x_{2}=2$ $1+1$ points

Read off coordinates of the intersection $(0,0)$ 1 point

Computationally verified solutions

$1+1$ points

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-16.jpg?height=380&width=528&top_left_y=758&top_left_x=227)