The function f(x) = –x3 + 2x2 – x + 5 is graphed on a coordinate grid. Which statements accurately describe the end behavior of the graph of the function?

answer my question first for ur answer

Step-by-step explanation:

The true statements about the graph of the function are:

The range of the function is {y : y ≤ 6} ⇒ 2nd

The function is increasing over the interval (–∞ , –2) ⇒ 3rd

The function has a positive y-intercept ⇒ 5th

Step-by-step explanation: Lets explain how to solve the problem

- The function f(x) = -x² - 4x + 2 is a quadratic function represented

 graphically by a downward parabola with maximum vertex

∵ The form of the quadratic function is f(x) = ax² + bx + c

∵ The coordinates of the vertex of the parabola are (h , k) where

  h = -b/2a and k = f(h)

∵ a = -1 , b = -4

∴ h = -(-4)/2(-1) = 4/-2 = -2

∵ k = f(h)

∴ k = -(-2)² - 4(-2) + 2 = -(4) - (-8) + 2

∴ k = -4 + 8 + 2 = 6

∴ The vertex of the parabola is (-2 , 6)

* Look to the attached figure to find the true statements

∵ The greatest value of the function is 6 ⇒ y-coordinate of the vertex

∵ The range of the function is the values y-coordinates of the points

 on the parabola

∴ The range of the function is {y : y ≤ 6}

- The domain of the function is {x : x ∈ R} or (-∞ , ∞)

∵ The value of y increasing after -∞ to the x-coordinate of the vertex

∵ x-coordinate of the vertex is -2

∴ The function is increasing over the interval (–∞ , –2)

- The parabola intersect the y-axis at point (0 , 2)

∵ The y-intercept is the intersection between the parabola and the

  y-axis

∵ The parabola intersect the y-axis at point (0 , 2)

∴ The y-intercept is 2

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is