Answer:
Over the interval [0, 2], the average rate of change of f is greater than that of g. The y-intercept of f is the same as the y-intercept of g.
Step-by-step explanation:
The function i.e mentioned in the question is
[tex]f(x)=5^x-4[/tex]
Now Placing x = 0, to compute the y-intercept
[tex]f(0)=5^(0)-4=1-4=-3[/tex]
f(x) y-intercept is -3
As we can see in the given graph the graph of g(x) intersects the y-axis at -3
Therefore the y-intercept of g(x) is -3.
Hence, both functions with respect to the y-intercepts i.e f(x) and g(x) would remain the same
Now At x=2,
So, the value of the function is
[tex]f(2)=5^2-4=25-4=21[/tex]
The average rate of change of f over the interval [0,2] is
[tex]m=\frac{f(2)-f(0)}{2-0}[/tex]
[tex]m=\frac{21-(-3)}{2}=12[/tex]
From the mentioned graph as we can see that the graph of g(x) is crossing through the points (0,-3) and (2,12).
The average rate of change of g over the interval [0,2] is
[tex]m=\frac{g(2)-g(0)}{2-0}[/tex]
[tex]m=\frac{12-(-3)}{2}=7.5[/tex]
Therefore this is the correct answer but the same is not provided in the given options
Answer:
Over the interval [0, 2], the average rate of change of f is greater than that of g.
Step-by-step explanation:
