Question

Consider two functions: g(x)=−x2−6x and the quadratic function ​f(x)​ shown in the table.

Which statements are true?

Select each correct answer.

Answer 1

1) The third option.

2) The last option.

Explanation:

1) f(x) is greater on the interval (0,3), which is opened, because if you substitute
`x=2` you obtain the following result

`f(2)=4\\g(2)=(2)^(2)-6(2)=-8`

3) If
`x=3`, you obtain that:

`g(3)=-9\\f(3)=9`

Therefore:
`f(3)>g(3)`

Answer 2

Answer : a, c, d

`g(x)= -x^2-6x`

x f(x) g(x)

-3 9 -27

-2 4 -16

-1 1 -7

0 0 0

-3 9 -27

-2 4 -16

-1 1 -7

(a) On the interval [0,3] f(x) is increasing and g(x) is decreasing. So rate of change of f(x) is greater than rage of change of g(x)

(b) f(x) and g(x) has same y intercept 0. so part b is not true

(c) f(x) is positive on the interval [0,3] . so f(x) is greater than g(x)

(d) g(3) = -27 and f(3) = 9. so g(3) is less than f(3)