Question

The graph of the function g(x) = -x is shown on the grid below.Graph the function h(x) = -x +2+3 in the interactive graph.←++-9-8-7-6-5-4-3-28886103219Y7+6+5+4+3.2.-2--3+-4+-5+-6+$7-8+69-9.2 3 4 5 6 7 8 9y= g(x)→x

Answer 1

A graph of the transformed absolute value function h(x) = -|x + 2| + 3 and its pre-image is shown in the picture below.

In Mathematics, the vertex form of the equation for an absolute value function can be modeled by the following:

y = a|x - h| + k.

Where:

• h and k are the vertex of the graph.
• a is a numerical constant.

By critically observing the equation of the transformed absolute value function, we can logically deduce that the parent absolute value function g(x) = -|x| was horizontally shifted to the left by 2 units, followed by a reflection in the x-axis, and then vertically shifted 3 units up as follows;

g(x) = a|x - h| + k.

h(x) = -g(x + 2) + 3

h(x) = -|x + 2| + 3

Answer 2

Given:

Given a graph of the function

`g(x)=-|x|`

Required:

To graph the function

`h(x)=-|x+2|+3`

Step-by-step explanation:

The graph of the function h(x) is,

The blue graph is the graph of the function h(x).

Final Answer: