Question

which statement compares the graphs of f(x) and g(x) over the interval [0, 5]?

A) The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5]

B) The graph of g(x) always exceeds the graph of f(x) over the interval [0, 5]

C) The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x)

D) The graph of g(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of f(x) exceeds the graph of g(x)

Answer 1

we can see that

For x is 0, 1, 2, 3 ,4

f(x) is  0 , 1 ,  4, 9 , 16

g(x) is -2 , -1 , 1 , 5 , 13

so, g(x) is greater than f(x) for x is 0, 1, 2, 3 ,4

It means that f(x) exceeds g(x) on [0,4]

But for x=5

f(x) is 25

g(x) is 29

Here, we can see that g(x) exceeds f(x) at x=5

so, there must be intersection point between x=4 and x=5

so, option-C.........Answer