Question

Which quadrants and axes does `f(x)=abs(x-6` pass through?

Answer 1

Both axes and the 1st and 2nd quadrant

Explanation:

We can start by thinking about `y=|x|` and how to transform it into the equation above.

We know the plot of `y = |x|` is basically just a big V with lines going along `y = x` and `y = - x`.

In order to get this equation, we shift `x` by 6. In order to get the tip of the V, we would need to plug in 6. However, other than that the shape of the function is the same.

Therefore, the function is a V centered at `x = 6`, giving us values in the 1st and 2nd quadrants, as well as hitting both the `x` and `y` axis.

Answer 2

The function passes through the first and second quadrants and passes through the `y` axis and touches the `x` axis

Explanation:

The graph of `f(x)=abs(x-6` is the graph of `f(x)=abs(x` shifted `6` units to the right.

Also, this is an absolute function meaning the `y` values are always positive so we can say that the range is `[0,oo)`.

Similarly, the domain is `(-oo,oo)`

Given this, the function passes through the first and second quadrants and passes through the `y` axis and touches the `x` axis.

Here's a picture of the graph below: graph{abs(x-6) [-5.375, 14.625, -2.88, 7.12]}