B2. Given the linear functions $f(x)=-x+1, g(x)=-4 x+4, h(x)=\frac{1}{3} x-2$.

(a) Draw the graphs of the linear functions in the same coordinate system (the unit should be $1 \mathrm{~cm}, \mathrm{k}$ label each line with its corresponding linear function).

(b) Write down the intersection point $P(x, y)$ of the functions $f$ and $g$.

(c) Which two functions are decreasing?

(d) Calculate the zero of the function $h(x)$.
B2.
(a)

![](https://cdn.mathpix.com/cropped/2024_06_07_a04162d2cc6b04e5d61eg-15.jpg?height=942&width=925&top_left_y=214&top_left_x=243)

(b) The $x$-coordinate of the intersection point is the solution to the equation $-x+1=-4x+4 \Rightarrow x=1$. The corresponding $y$-coordinate is $-x+1=-1+1=0$. The intersection point $P$ is $P(1,0)$.

(c) The functions $f$ and $g$ are decreasing because they have negative slope coefficients.

(d) The zero of the function $h$ is the solution to the equation $h(x)=0$ or $\frac{1}{3} x-2=0$. The solution is $x=6$.

a) Each correctly drawn graph earns 1 point, totaling 3 points. ..........................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_a04162d2cc6b04e5d61eg-15.jpg?height=54&width=1742&top_left_y=1658&top_left_x=174)

![](https://cdn.mathpix.com/cropped/2024_06_07_a04162d2cc6b04e5d61eg-15.jpg?height=48&width=1742&top_left_y=1712&top_left_x=174)

d) Writing the equation $\frac{1}{3} x-2=0$. ............................................................................................................................

Calculating the zero $x=6$. .........................................................................................................