Question

State if the following is a function. f(x)=|x-3|

Answer 1

Answer:

  Yes

Step-by-step explanation:

The absolute value function is a function. Translating its graph 3 units to the right does not change that. It has one output for each input.

Answer 2

Answer:

Yes

Step-by-step explanation:

In a function, each input has a single output. The absolute value function is already a function.

The function:

$f(x)= | x-3|$

The -3 translates the function 3 to the right, but it remains a function.

The photo of the graph also shows it is a function. It passes the vertical line test. If you draw a vertical line anywhere on the graph, the line and graph should only touch once.