Question

Write the function shown on the graph

Answer 1

Answer: $g(x)=|x|+3$

Step-by-step explanation:

By definition, the Absolute Value parent function has the following form:

$f(x)=|x|$

The vertex of the graph is at the point (0,0)

It is important to remember the following transformations for a function:

If $f(x)+k$, then the function is shifted "k" units up.

If $f(x)-k$, then the function is shifted "k" units down.

If $f(x+k)$, then the function is shifted "k" units left.

If $f(x-k)$, then the function is shifted "k" units right.

Let be g(x) the function shown in the graph provided in the exercise.

You can observe that its Vertex is at the point (0,3).

Therefore, you can conclude that the function g(x) is obtained by shifting the Absolute Value parent function 3 units up.

Then, this is:

$g(x)=|x|+3$