Make a table of values for f(x) = x after the given translation 4 units down

See the attached.

Step-by-step explanation:

Translating a function up or down is simply a matter of adding or subtracting a value to/from the function. To translate f(x) 4 units down, subtract 4 from it.

original function: f(x) = x

function translated down 4 units: g(x) = f(x) -4 = x - 4

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc