Given a function f(x) we translate the function:
• a units horizontally (a > 0 to the right, a < 0 to the left),
,• b units vertically (b > 0 up, b < 0 down),
by the transformation:
In this case, we have:
Comparing f(x) and g(x) with the general transformation above, we see that the graph of g(x) is the graph of f(x) translated:
• a = 2 units to the right,
,• b = 4 units up.
Translating the graph of f(x), we get:
AnswerThe translated graph is the graph in red:
Equation of the circle is .
Solution:
The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).
Center of the circle = Mid point of the diameter
Mid point formula:
Here,
Center of the circle = (–6, –10)
Radius is the distance between center and any endpoint of the diameter.
To calculate the radius using distance formula.
Here,
units
The standard form of the equation of a circle is
, where (a, b) are center and r is the radius.
Here, center = (–6, –10) and
Equation of the circle is .