write the domain and range of the function.

Question

h(x)= -|x+1|+2

Answer 1

The main things to look for in finding the domain, or possibilities of an x-values or input, are that we can't take the square root of a negative number, nor have a denominator of 0.

Looking at what we have, any value of x works, so the domain is x = all real numbers, or (-∞,∞) orrr -∞ ≤ x ≤ ∞.

As far as the range, or possibilities of y-values or output, we know that absolute value is always positive (absolute value is the distance from 0 and we measure using positive numbers), though the negative sign in front of it will make it negative.

The smallest distance from 0 is 0, right? Either direction from 0 has a greater absolute value than zero.

Buuuut, we have a negative sign, so our value will get smaller as our absolute value gets larger. If the absolute value is 100, we get -100, for example.

The point being that the largest our negative absolute value will be is 0. Then, we get to add 2 to it. If the largest value we add 2 to (hey, are you a ballerina?) Is 0, then the largest value our output can be is 2.

y ≤ 2 or (-2,2] or -∞ ≤ y ≤ 2

Hopethis helps!

Answer 2

First lets look at the domain. Can we plug any number into this function? Yes, therefore the domain, is all real numbers. Next the range. What is the largest -|x+1| can be? 0, therefore the maximum this can be is 2. So we have a domain of (-inf,inf) and a range of (-inf,2]

Answer 3

Given the function, we can find the domain and range by determining what is possible for x and y values.

There is nothing restricting you from having any x value because any number inserted for x would result in a real solution. Therefore, the domain is all real numbers.

This function uses x inside an absolute value so it takes the shape of a V

The base of this graph ( |x+1| ) would look like an upright V with a slope of 1 to the left and right. This function is reflected about the x-axis as a result of its negative/opposite sign beforehand, meaning it is facing down

It is also translated (moved) up two points as a result of the +2

Knowing its translation and direction, we know none of the y-values are above 2, meaning the range is all real numbers 2 and lower