Question

On each coordinate plane,the parent function f(x)=|x| is represented by a dash line translation is represented by a solid line. Which graph represents the The translation g(x)=|x+2| as a solid line?

Answer 1

It passes to the y-axis and not the x-axis at the point four. The graph represents that it should be increasing at the slope of the point one.

Answer 2

Refer the attached graph.

Explanation:

Given : On each coordinate plane,the parent function
`f(x)=|x|` is represented by a dash line translation is represented by a solid line.

To find : Which graph represents the the translation
`g(x)=|x+2|` as a solid line?

Solution :

The parent function
`f(x)=|x|`

with the vertex (0,0)

And the graph of
`g(x)=|x+2|`

with the vertex (-2,0)

The graph of g(x) is the translation of f(x)

The parent function is translated towards left.

Transformation to the left,

f(x)→f(x+b) , the graph of f(x) is shifted towards left by b unit.

Same as the graph f(x) is shifted towards left by 2 unit and form graph of g(x).

We plot the graph of both the equations in which translation is shown.

Refer the attached graph below.