functions within functions (1 Viewer)

[user18181818]

why is it a not b?

 

[AsuTeksu]

Since the function is g(f(x)), this mean that when you substitute an x-value into f(x), the output of f(x) is the input for g(x) which will form the graph.

At point x = a, f(a) = 0, so from this we use the output of 0 as the x-value for g(x), and g(0) is approximately 0.5, hypothetically. This is why there shouldn't be any asymptote at x = a.

You would repeat this process with other points and ultimately, you'll get the graph of A.

 

[AsuTeksu]

^ i have no idea if that even makes sense so,,, rip-

 

[smiley_riley]

You can think about with just testing points.
Test x = a. f(a) = 0, therefore g(f(a)) = g(0), you can see that g(0) is a small positive number,
so it works with answer A and not B.

 

[smiley_riley]

^ i have no idea if that even makes sense so,,, rip-

You would answer two seconds before I did

 

[user18181818]

but g(0) is a small number for both functions thats why im confused

 

[AsuTeksu]

but g(0) is a small number for both functions thats why im confused

What do you mean?

Let's say that hypothetically, g(0) = 0.5, so that means on the graph of g(f(x)), at point a, y = 0.5

 

[smiley_riley]

but g(0) is a small number for both functions thats why im confused

There is only one g(x) function which is the one on the top of the page. The g(0) we're looking at is the one in the top right.
while the answers are functions g(x). the x is not the same as it's replaced with f(x).

 

[user18181818]

ahhh got it now thanks!

 

[Luukas.2]

The only way that g(f(x)) will have a vertical asymptote is if g(f(x)) = g(a), and so there would need to be some x-value such that f(x) = a.

Look at the graph, f(x) is always positive or zero, but a is negative. f(x) = a has no solution. So, g(f(x) won't have a vertical asymptote, and the answer can't be (B), (C), or (D).