Question

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

Answer 1

Answer:

The graph shifts 7 units left and 2 units up.

Step-by-step explanation:

In transformations, when a number is added or subtracted to "x" directly, that is the left/right shift.

When a number is added or subtracted outside of the "rest" of the equation, that is the up/down shift.

I learned transformations with these variables:

$f(x) = \frac{a}{k(x-c)} + d$

"a" - vertical stretch (a > 1) or compression (0 < a < 1)

"k" - horizontal stretch (0 < k < 1) or compression (k > 1)

"c" - translate left (+) or right (-)

"d" - translation up (+) or down (-)

The untranslated graph is centred around the origin f(x) = 1/x

f(x) begins 3 units right and 1 unit up of the untranslated graph.

g(x) is 4 units left and 3 units up of the untranslated graph.

            y

g           |

            |           f

-----------|------------ x

There is a 7 units translation left and 2 units translation up.

Answer 2

The graphs shifts 7 units up and 2 units up