Question

How do you graph, find the zeros, intercepts, domain and range of `f(x)=abs(x)+4`?

Answer 1

The y-intercept is `y=4` and there are no x-intercepts.
The domain is all real numbers and the range is `y>=4`.

Explanation:

How to Graph:

Luckily, this is a (somewhat) linear graph. Firstly, we should identify the `|quad|`. If you want the in-depth definition, an absolute value is only the distance from the number to 0. For example, the distance from -4 and 0 is 4, therefore x is 4.

If you want a easier explanation, it's basically all x-values become positive. If you plug in 1 for x, it will equal 5 because 1+4=5. If you plug in -1, it will equal 5 again since the -1 becomes 1 due to the absolute value rule.

This becomes somewhat of an equation that looks like this `y=x+4` but the left side is also positive so the graph should look like a linear v with a slope of one.

Zeroes:

As for the zeroes, there are none. This is because it's impossible for `y=0` since if you try to plug in -4, it will simply become 4 and the y-value will be 8. Therefore there are no x-intercepts/zeroes.

For the y-intercept, plug in 0 for x then add four then you'll get y=4.

Domain/Range:

The domain is all real numbers, because any number can be plugged in without getting a "error" or "undefined" answer. (An example of undefined is plugging in 0 for a denominator in a fraction.)

The range is `y>=4` because the lowest point of the graph is 4 (this is since the graph can't go any lower due to the absolute value sign). However, the graph can go infinitely higher since any x-value can be plugged in and the y-value will increase (even if the x-value is negative since absolute value). Even an extremely large x-value can be plugged in for an extremely large y-value (in the millions, billions, trillions etc.).