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For the basic function f(x)=x, what conclusions can you make about f(x) and f(x)-5? Select all that apply.

A. The y-intercepts are the same.

B. The function f(x)-5 has a greater rate of change.

C. They are parallel lines.

D. The graph of the function f(x) I’d translated down 5 units to produce f(x)-5

Answer :

Answer:The ansewers are c and d.

Step-by-step explanation:

The function f(x)=x is really y=x.

The graph of function [tex]f(x)=x[/tex] and [tex]f(x)-5[/tex] are straight lines and they are parallel.

[tex]f(x)-5[/tex] is  a line that produce after translate 5 unit down of graph of [tex]f(x)=x[/tex]

Therefore, option (C) and (D) both are correct.

Given function are,  

                             [tex]f(x)=x\\\\f(x)-5=x-5[/tex]

After comparing above equation from, [tex]y=mx+c[/tex] , where m is slope of line.

It is observed that both lines have same slope. Therefore, they are parallel lines.

And  graph of the function[tex]f(x)[/tex]  translated 5 units down to produce [tex]f(x)-5[/tex]

Therefore, option (C) and (D) both are correct.

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