Question

Two functions question.

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

A) The maximum y-value of f(x) approaches 2.
B) g(x) has the largest possible y-value.
C) f(x) has the largest possible y-value.
D) f(x) and g(x) have equivalent maximum y-values.

There can be multiple answers.

Answer 1

A and D
Picturing the graph, y=2^x is the parent function, which is infinitely close to 0 on the left and shoots up to infinity somewhere on the right
Making it y=5^x just makes it steeper
Putting a negative in the front flips the graph over the x axis
and the +2 then moves it up two
So you've got something that looks like it starts around 2ish on the left, and then drops down to negative infinity on the right
A is true because of the way an exponential graph works, and D is also true because they are the same graph
You know B and C can't be true because they are the same graph, therefore neither can have greater y values

Answer 2

Thanks Scorcher! You're the man! I'm definitely getting a more thorough understanding of this material now.

Answer 3

No problem! I'm happy to help