Question

Given the functions ƒ(x) and g(x), which of the following statements is true? x -2 -1 0 1 2 ƒ(x) -3 3 5 3 -3 g(x) = -x2 + 4x ƒ(x) has the greater maximum. g(x) has the greater maximum. ƒ(x) and g(x) have the same maximum.

Answer 1

ƒ( x) has the greater maximum.

Explanation:

Answer 2

The correct option is 1.

Explanation:

From the given table is notices that the function f(x) is a downward parabola.

The maximum value of f(x) is 5 at x=1.

The function g(x) is

`g(x)=-x^2+4x`

vertex of the parabola is

`((-b)/(2a), g((-b)/(2a)))`

`((-4)/(2* 1), g((-4)/(2* 1))`

`(2, g(2))`

Put x=2.

`g(x)=-2^2+4(2)=4`

Therefore the vertex of g(x) is (2,4). The vertex of a downward parabola is the maximum point of the function.

Therefore ƒ(x) has the greater maximum. Option 1 is correct.