What can you say about the y-values of the two functions f (x) = -5^x + 2 and g (x) = -5x^2+2?

A) f (x) and g (x) have equivalent maximum values

b) The maximum y-value of f (x) approaches 2

c) g (x) has the largest possible y-value

d) f (x) has the largest possible y-value

Its multiple choice

B) The maximum y-value of f (x) approaches 2

C) g (x) has the largest possible y-value

Step-by-step explanation:

f (x) = -5^x+2

f (x) is an exponential function.

Lim x→∞ f (x) = Lim x→∞ (-5^x+2) = - 5^ (∞) + 2 = - ∞+2→ Lim x→∞ f (x) = - ∞

Lim x→ - ∞ f (x) = Lim x→ - ∞ (-5^x+2) = - 5^ (-∞) + 2 = - 1/5^∞+2 = - 1/∞+2 = 0+2→

Lim x→ - ∞ f (x) = 2

Then the maximun y-value of f (x) approaches 2

g (x) = -5x^2+2

g (x) is a quadratic function. The graph is a parabola

g (x) = ax^2+bx+c

a=-5<0, the parabola opens downward and has a maximum value at

x=-b / (2a)

b=0

c=2

x=-0/2 (-5)

x=0/10

x=0

The maximum value is at x=0:

g (0) = -5 (0) ^2+2=-5 (0) + 2=0+2→g (0) = 2

The maximum value of g (x) is 2