Let f(x) = x + 4 and g(x) = x − 3. If g is a vertical translation of f, how many units and in what direction is f translated to form g? number of units: direction of translation:

Answer 1

Let's compare f(x) and g(x):

f(x) = x + 4

g(x) = x - 3

Both f(x) and g(x) are linear functions in slope-intercept form. They both have the same slope, with the only difference being their y-intercept.

Therefore, we can see that g(x) is a vertical translation of f(x) by -7 units. In other words, g(x) is translated 7 units down from f(x).

In general, if f(x) is a parent function, and g(x) is a transformation of f(x) written as g(x) = f(x) + a, then a describes a vertical translation of f(x).

1. If a is positive, it's translated "up".
2. If a is negative, it's translated "down".

Therefore, we can calculate the specific translation algebraically:

1. g(x) = f(x)+ a
2. x - 3 = x + 4 + a
3. -7 = a

Therefore, we can represent g(x) as f(x) - 7.

Just an added note, but translations are a type of transformation called a "rigid" transformation, which you will see a lot more in Geometry. A rigid transformation is one that preserves the congruency of the shape, hence the term rigid.

Answer 2

g(x) - f(x)

x - 3 - (x + 4)

x - 3 - x - 4

-7