The new equation will be:
[tex]g(x) =\frac{1}{x+4}+4[/tex]
OR
[tex]g(x) = \frac{x+5}{x+4}[/tex]
Step-by-step explanation:
The function transformations are defined as:
Shifting function upwards b units
[tex]f(x) => g(x) = f(x)+b[/tex]
Shifting functions to the left b units
[tex]f(x) => g(x) = f(x+b)[/tex]
Given function is:
[tex]g(x) = \frac{1}{x}[/tex]
Shifting the function 4 units to the left will give us:
[tex]g(x) => g(x+b)\\= \frac{1}{x+4}[/tex]
Now shifting the function 4 units upwards
[tex]g(x) = \frac{1}{x+4} + 4[/tex]
Simplifying
[tex]g(x) = \frac{1+x+4}{x+4}\\= \frac{x+5}{x+4}[/tex]
The new equation will be:
[tex]g(x) =\frac{1}{x+4}+4[/tex]
OR
[tex]g(x) = \frac{x+5}{x+4}[/tex]
Keywords: function, transformations
Learn more about functions at:
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