Math, asked by elijahjones0702, 10 months ago

The graph of the function f(x) = (x – 4)(x + 1) is shown below.

Answers

Answered by amitnrw
4

Given :   f(x) = (x – 4)(x + 1)

To Find : Which statement about the function is true?

It goes through (negative 1, 0)

has a vertex at (1.75, negative 6.2)

goes through (4, 0).

The function is increasing for all real values of x where x  > 4.

The function is decreasing for all real values of x where –1 < x < 4.

The function is decreasing for all real values of x where x < 1.5.

Solution:

f(x) = (x – 4)(x + 1)

x = - 1 => f(x) = 0 hence  goes through (negative 1, 0)

x = 4 => f(x) = 0 hence  goes through (4, 0)

=> f(x) = x²  - 3x  - 4

= (x - 1.5)² - 6.25

Hence vertex is  ( 1.5 , 6.25)

has a vertex at (1.75, negative 6.2) - FALSE

f'(x) = 2x - 3

The function is increasing  if 2x - 3 >  0

=> x > 3/2

The function is increasing for all real values of x where x > 1.5

Hence this is also true The function is increasing for all real values of x where x  > 4

The function is decreasing for all real values of x where x <  1.5

The function is decreasing for all real values of x where x < 1.5. TRUE

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