1. The problem asks to apply sequential transformations to the graph of $y=3x$ and write the resulting equation at each step. 2. Start with the original function: $$y=3x$$ 3. (a) Shift the graph 2 units downward. This means subtract 2 from the function: $$y=3x-2$$ 4. (b) Shift the graph 1 unit to the right. Replace $x$ by $x-1$: $$y=3(x-1)-2=3x-3-2=3x-5$$ 5. (c) Reflect the graph about the x-axis. Multiply the entire function by $-1$: $$y=-(3x-5)=-3x+5$$ 6. (d) Reflect the graph about the y-axis. Replace $x$ by $-x$: $$y=-3(-x)+5=3x+5$$ Final transformed function after all steps is: $$y=3x+5$$