Question

Determine which graph, f(x)=square root of 16x or g(x)=16square root of x, rises more steeply. Explain

Answer 1

`16√(x)`

Explanation:

Compare the graphs in the attached picture. The red graph is
`√(16x)`. The blue graph is
`16√(x)`. The blue rises much steeper.

Answer 2

g(x) rises more steeply than f(x)

Explanation:

Given:
`f(x)=√(16x)`

`g(x)=16√(x)`

The parent function of both f(x) and g(x) is same.

`\text{Parent function }:p(x)=√(x)`

`f(x)=√(16x)=4√(x)`

`g(x)=16√(x)`

`y=a\cdot f(x)`

The rise of function depends on the value of a.

Higher the value of a rises more because coefficient is more.

`p(x)=√(x)`

`f(x)=4√(x)`

`g(x)=16√(x)`

The coefficient of g(x) is more than f(x).

We can see graphically also. Please see attachment for graph.

Hence, g(x) rises more steeply than f(x).