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

On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).

Which statement about the function is true?

The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and 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.

The graph of the function fx x 4x 1 is shown below On a coordinate plane a parabola opens up It goes through negative 1 0 has a vertex at 175 negative 62 and go class=

Respuesta :

Ashraf82

Answer:

The function is decreasing for all real values of x where  x < 1.5 ⇒ 4th

Step-by-step explanation:

* Lets revise some points about the quadratic function

- The quadratic represented graphically by a parabola

- If the vertex of the parabola is point (h , k), then

- Point (h , k) is the minimum point of the function if the parabola opens

   upward

- Point (h , k) is the maximum point of the function if the parabola opens

   downward

- If point (h , k) is a minimum point, then the function is decreasing

  for all values of x smaller than h and increasing for all values of x

  greater than h

- If point (h , k) is a maximum point, then the function is increasing for

   all values of x smaller than h and decreasing for all values of x greater

   than h

* Now lets solve the problem

- From the attached graph and the given

∵ The parabola represents a quadratic function

∵ The parabola opens upward

∴ Its vertex is minimum

- Lets use the bold point above

∵ The coordinates of the vertex are (1.75 , -6.2)

∴ The function is decreasing for all values of x less than 1.75

* The function is decreasing for all real vales of x where x < 1.75

∴ The function is increasing for all values of x greater than 1.75

* The function is increasing for all real vales of x where x > 1.75

- From the answer there is only one statement true

- The statement is:

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

   because the function is decreasing for all real values of x where

    x < 1.75 and 1.5 is smaller than 1.75

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

ashishdwivedilVT

The function is increasing for all real values of x where

x < –1 and where x > 4.

Given function is

[tex]f(x) =(x-4) (x+1)[/tex]

If f(x) = 0,  x=4 & x=-1

f'(x) = 0, x=3/2

So, we will check the behavior of the function in the neighborhood of  x=4,-1, 3/2.

What is the increasing and decreasing function?

A function is said to be an increasing function if its slope is continuously increasing in a given interval.

A function is said to be a decreasing function if its slope is continuously decreasing in a given interval.

If x>4

Let us check at x=5

f(5) =6(+ve)

f(x) >0 for x>4

So, the function is increasing in x>4

Similarly, If x <-1

f(x) >0 for  x <-1

So, function is increasing in x <-1

If -1<x<3/2

f(x)<0 for -1<x<3/2

So, function is decreasing in -1<x<4

If 3/2<x<4

f(x)>0 for 3/2<x<4

So, the function is increasing in 3/2<x<4

From the graph too, we can see the behavior of the given function

by observing the slope.

We can see that for x<-1 and x>4, the slope is continuously increasing

So, the function is increasing in x<-1 and x>4.

Therefore, the function is increasing for all real values of x where

x < –1 and where x > 4.

To get more about increasing and decreasing functions visit:

https://brainly.com/question/11861192

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