Let us calculate the y-intercepts and average rate of change over the given intervals.
Function F
[tex]f(x)=5^x-4[/tex]
The y-intercept is gotten at x = 0:
[tex]\begin{gathered} f(0)=5^0-4=1-4 \\ f(0)=-3 \end{gathered}[/tex]
The average rate of change can be calculated using the formula:
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
Using [0, 2] as [a, b], we have:
[tex]\begin{gathered} f(0)=-3 \\ f(2)=5^2-4=25-4=21 \end{gathered}[/tex]
Therefore, we can solve to give:
[tex]\begin{gathered} m_f=\frac{21-(-3)}{2-0}=\frac{24}{2} \\ m_f=12 \end{gathered}[/tex]
Function G
The graph is given in the question.
The y-intercept is approximately -3.
The average rate of change can be calculated using the following parameters;
[tex]\begin{gathered} f(a)=-3 \\ f(b)=13 \end{gathered}[/tex]
Therefore, we can solve to give:
[tex]\begin{gathered} m_g=\frac{13-(-3)}{2-0}=\frac{16}{2} \\ m_g=8 \end{gathered}[/tex]
CONCLUSION
The two graphs have the same y-intercept.
The average rate of change in graph g is less than f.
The correct option is OPTION B.
