ANSWER and EXPLANATION
We want to plot the points where the given function crosses the x and y axes:
[tex]g(x)=-5^x+5[/tex]The graph of a function crosses the x-axis at the point where g(x) = 0 and it crosses the y-axis at the point where x = 0.
This means that we have to find the value of the function when x = 0 and when g(x) = 0.
When x = 0:
[tex]\begin{gathered} g(x)=-5^0+5 \\ g(x)=-1+5 \\ g(x)=4 \end{gathered}[/tex]Therefore, the function crosses the y-axis at (0,4).
When g(x) = 0:
[tex]\begin{gathered} 0=-5^x+5 \\ \Rightarrow5^x=5 \\ \Rightarrow5^x=5^1 \\ Since\text{ the base on both sides are the same:} \\ x=1 \end{gathered}[/tex]Therefore, the function crosses the x-axis at (1,0).
Let us plot the two points:
NOTE: The blue point represents where the function crosses the y-axis while the green point represents where the function crosses the x-axis.
