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consider the function.
f(x) = 2x - 6

1) shifts f(x) 4 units down  = g(x) =

2) stretches by factor 4    =  g(x) =

3) shifts f(x) 4 units right   =  g(x) =

4) compresses by factor 4 =  g(x) =

Step-by-step explanation:

1) When we have to move the function down by 4 units, subtract the whole function by -4, that is y -4.

Thus, f(x) becomes  g(x) = =

2) When the function is stretched away from x axis, it means in Y direction.

 Thus, when stretched 4 units in Y direction, the function becomes 4(f(x))

 =  g(x) = =

3)When we have to move the function right by 4 units, replace x with (x-4) in the function.

Thus, f(x) becomes  g(x) = = =

4) When the function is stretched towards y axis, it means in X direction.

 Thus, when compressed 4 units in X direction, replace the x by 4x.

 =  g(x) = =

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

the radius is 2 times the diameter.

step-by-step explanation: