Question

compare the functions in the table as the value of x increases which function will eventually exceed the value of th other functions A. y=5x b. y=x^5 c. y=3x^3 + 10 d. y= 1000x^3 + 1

Answer 1

Option b: y = x^5

Explanation:

The functions are:

a) y = 5*x

b) y = x^5

c) y = 3*x^3 + 10

d) y = 1000*x^3 + 1

This is really simple, here we need to know that when we have powers of x:

x^n and x^m

The one with the larger exponent will grow faster (specially for larger values of x)

Only with this, we can guess that the correct option is b.

But let's check that.

The other function that has the largest exponent (and also a very large coefficient) is option d

y = 1000*x^3 + 1

Now, if we evaluate both functions b) and d) in x = 1000, we get:

b) y = 1000^5

While in option d we have:

d) y = 1000*1000^3 + 1 = 1000^4 + 1

And clearly:

1000^5 > 1000^4 + 1

For larger values of x, this difference will be larger (you could also compare the function y = x^5 with the other ones for this value of x, and in all the cases you will see that option b is the larger one).

Then the correct option is b.