College

The graph of the function [tex]y=f(x)+93[/tex] can be obtained from the graph of [tex]y=f(x)[/tex] by one of the following actions:

A. Shifting the graph of [tex]f(x)[/tex] upwards 93 units
B. Shifting the graph of [tex]f(x)[/tex] to the left 93 units
C. Shifting the graph of [tex]f(x)[/tex] to the right 93 units
D. Shifting the graph of [tex]f(x)[/tex] downwards 93 units

Answer :

Consider the function

[tex]$$
y = f(x) + 93.
$$[/tex]

This equation is obtained by taking the original function [tex]$f(x)$[/tex] and adding [tex]$93$[/tex] to its output values. In terms of transformations, adding a constant to the entire function results in a vertical shift. Specifically, adding [tex]$93$[/tex] shifts the graph of [tex]$f(x)$[/tex] upward by [tex]$93$[/tex] units.

To summarize the steps:

1. We start with the original graph [tex]$y = f(x)$[/tex].
2. Adding [tex]$93$[/tex] to the function gives the new graph: [tex]$y = f(x) + 93$[/tex].
3. This simply means every [tex]$y$[/tex]-value in the original graph is increased by [tex]$93$[/tex], which moves the graph upward by [tex]$93$[/tex] units.

Thus, the correct transformation is:

[tex]$$
\text{Shifting the graph of } f(x) \text{ upwards 93 units.}
$$[/tex]

The final answer is option 1.