Question

Which compares the end behavior of the functions f and g?

f(x) = −17x − 9 g(x) = − 78
7
8
x + 20
A. For function f, as x → ∞
x

→

∞
, f(x) → ∞
f
(
x
)

→

∞
. Likewise, for function g, as x → ∞
x

→

∞
, g(x) → ∞
g
(
x
)

→

∞
.
B. For function f, as x → ∞

x

→

∞
, f(x) → −∞
f
(
x
)

→

−
∞
. Likewise, for function g, as x → ∞
x

→

∞
, g(x) → −∞
g
(
x
)

→

−
∞
.
C. For function f, as x → ∞
x

→

∞
, f(x) → −∞
f
(
x
)

→

-
∞
. However, for function g, as x → ∞
x

→

∞
, g(x) → ∞
g
(
x
)

→

∞
.
D. For function f, as x → ∞

x

→

∞
, f(x) → ∞

f
(
x
)

→

∞
. However, for function g, as x → ∞
x

→

∞
, g(x) → −∞
g
(
x
)

→

−
∞
.

Answer 1

The correct option that compares the end behavior of the functions f and g is D.

For function f, as x → ∞, f(x) → -∞, which means that the function approaches negative infinity as x approaches infinity. This is because the leading term of the function is -17x, which approaches negative infinity as x approaches infinity.

For function g, as x → ∞, g(x) → -∞, which means that the function also approaches negative infinity as x approaches infinity. This is because the leading term of the function is -78/87x, which approaches negative infinity as x approaches infinity.

Therefore, both functions have the same end behavior, which is approaching negative infinity as x approaches infinity.