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Given the functions f(x)= 1/x−4 +3 and g(x)=1/x+1 +6 .


Which statement describes the transformation of the graph of function f onto the graph of function g?



The graph shifts 5 units right and 3 units down.


The graph shifts 3 units left and 5 units up.


The graph shifts 5 units left and 3 units up.


The graph shifts 3 units right and 5 units down.

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kudzordzifrancis

ANSWER

The graph shifts 5 units left and 3 units up.

EXPLANATION

The given functions are:

[tex]f(x) = \frac{1}{x - 4} + 3[/tex]

and

[tex]g(x) = \frac{1}{x + 1} + 6[/tex]

We want to transform f(x) so that, it coincide with the g(x).

The required transformation is

[tex]f(x+5)+3[/tex]

Let us see why this works.

[tex]f(x+5)+3 = \frac{1}{x + 5- 4} + 3 + 3[/tex]

[tex]f(x+5)+3 = \frac{1}{x + 1} + 6 = g(x)[/tex]

The transformation f(x+5)+3 will shift f(x) 5 units left and 3 units up.

The third choice is correct.

alinakincsem

Answer with step-by-step explanation:

We are given a function [tex]f(x) =  \frac{1}{x - 4}  + 3[/tex] which is to be transformed to another function [tex]g(x) =  \frac{1}{x + 1}  + 6[/tex].

We are to determine whether which statement describes the transformation of the graph of function f onto the graph of function g.

[tex]f(x+5)+3 = \frac{1}{x + 5- 4}  + 3 + 3[/tex]

[tex]f(x+5)+3 = \frac{1}{x + 1}  + 6[/tex]

[tex]f(x)=g(x)[/tex]

Therefore, the correct answer option is: The graph shifts 5 units right and 3 units up.

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