Select the correct answer.
The function g(x) = x2 is transformed to obtain function h:

h(x) = g(x) + 1.

Which statement describes how the graph of h is different from the graph of g?

A.
The graph of h is the graph of g vertically shifted down 1 unit.
B.
The graph of h is the graph of g vertically shifted up 1 unit.
C.
The graph of h is the graph of g horizontally shifted right 1 unit.
D.
The graph of h is the graph of g horizontally shifted left 1 unit.

Respuesta :

Answer:

the answer is D

Step-by-step explanation:

The graph of h is the graph of g horizontally shifted left 1 unit.

Given that,

The function [tex]\rm g(x) = x^2[/tex]is transformed to obtain function h:

h(x) = g(x) + 1.

We have to determine,

Which statement describes how the graph of h is different from the graph of g?

According to the question,

The first transformation is vertical transformation.

This type of transformation shifts the graph up or down relative to the parent graph.

The graph will shift up if we add a positive constant to each y- coordinate whereas the graph will shift down if we add a negative constant.

This type of transformation shifts the left or right relative to the parent graph.

This takes place when we add or subtract coordinates from the x-axis before the function is applied.  

The h(x) is horizontally shifted left 1 unit

The equation is,

[tex]\rm h(x) = g(x)-1[/tex]

The h(x) is horizontally shifted left 1 unit,

The equation is,

[tex]\rm h(x) = g(x)+1[/tex]

Hence, The graph of h is the graph of g horizontally shifted left 1 unit.

To know more about Transformation of Graph click the link given below.

https://brainly.com/question/21981889