To translate the graph of a function is part of Rigid Transformations because the basic shape of the graph is unchanged
[tex]Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:[/tex]
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c[/tex]
[tex]\bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]
In this case, we have the graph of:
[tex]y=x[/tex]
And we need to translate it to make it the graph of:
[tex]y=x-1+4[/tex]
According to our rules we need:
But [tex]y=x-1+4[/tex] is the same as [tex]y=x+3[/tex], so the previous steps can be simplified as:
Below are shown those graphs:
Shifting graphs: https://brainly.com/question/10010217
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