Please help m from edge about graphing an absolute value function

determine the domain and range of the function f(x)= -|x| + 2.
the domain of the function is
the range of the function is

the options are: all real numbers, all numbers greater than or equal to 2, and all numbers less than or equal to 2

For the given function f(x)= -|x| + 2

the domain of the function is: All real numbers

the range of the function is: all numbers greater than or equal to 2

Step-by-step explanation:

We need to find the domain and range of the function f(x)= -|x| + 2.

Domain: Domain is defined as all the possible x values of x for which the function is true.

Range: Range is defined as all the possible y values.

So, For the given function f(x)= -|x| + 2

the domain of the function is: All real numbers (the function is true for all real numbers)

the range of the function is: all numbers greater than or equal to 2

(When solving the equation we will have value of f(x) equal or greater than 2)

whats the

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!