Based on the graph of the functions, which of the following statements is true?

a.
f(x) eventually exceeds g(x) because f(x) is increasing linearly
b.
at x = 13, the value of f(x) is more than the value of g(x).
c.
g(x) eventually exceeds f(x) because g(x) is increasing exponentially
d.
over the interval [3, 5], the average rate of change of g is greater than the average rate of change of f.

  C.  g(x) eventually exceeds f(x) because g(x) is increasing exponentially

Step-by-step explanation:

Comments on the other choices:

  A -- an exponential function eventually exceeds any polynomial function. (A linear function is a polynomial of degree 1.)

  B -- at x=13, f(x) = 17; g(x) ≈ 18.2, so g(x) is more

  D -- over the given interval, the average rate of change of g(x) is about 1/2 (1 unit rise for 2 units run) compared to the slope of 1 that f(x) has.

step-by-step explanation:

∠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.