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

Answer:

The correct option is 1.

Step-by-step 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

$(\frac{-b}{2a}, g(\frac{-b}{2a}))$

$(\frac{-4}{2\times 1}, g(\frac{-4}{2\times 1})$

$(2, g(2))$

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.