Question

a student is tasked with the graphing f(x) =1/x+3 -4. he notes that the graph is a merely translation not f(x) =1/x, requiring shift shift of three units horizontally followed by a shift of four units vertically. is the student correct?

Answer 1

The general equation for translating is expressed as:

g(x) = f(x - a) + b

where a = horizontal shift

b = vertical shift

Given the function

$f(x)\text{ = }\frac{1}{x+3}-4$

On comparing with the standard equation, we can see that

b = -4

which shows that the translation requires a vertical shift of four units (downwards)

also

x-a = x+3

On comparing

a = -3

this shows that the translation requires a horizontal shift of 3 units (towards the left being negative)

Hence the student is correct. The x-3 in 1/x+3 implies a leftwrad shift of 3units and a constant -4 implies downward shift of 4units