Question

How are the graphs of the functions f(x) = and g(x) =related?

The functions f(x) and g(x) are equivalent.
The function g(x) increases at a faster rate.
The function g(x) has a greater initial value.
The function g(x) decreases at a faster rate.

Answer 1

I can't see the actual formulas for f(x) and g(x) — they were omitted. Please paste them.

Meanwhile, here are quick rules that will let you pick the correct choice once you give the functions:

- For exponentials of the form A·b^x:
- initial value (y-intercept) = A·b^0 = A. So a larger coefficient A gives a greater initial value.
- if 0 < b1, b2 < 1 both decay; the smaller base (closer to 0) decays faster.
- if b1, b2 > 1 both grow; the larger base grows faster.
- if b1 = b2 and A1 = A2 the functions are equivalent.

- For linear functions mx + b:
- initial value = b.
- growth/decay rate is determined by slope m (larger m = increases faster; negative m = decreases).

- For other types, compare leading coefficients and exponents to determine initial value and rate.

If you paste f(x) and g(x) I’ll pick the right option and show the brief reasoning.