Question

Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.

Answer 1

`\huge \boxed{k=4}`

Explanation:

The graph of g(x) crosses the point (1, 10).

The graph of f(x) crosses the point (4, 10).

So, g(1) = 10. The x (input) is 1. The output is 10.

f(4) = 10. The x (input) is 4. The ouput is 10.

g(1) = f(4)

g(x) = f(k ⋅ x)

g(1) = f(k ⋅ 1)

f(k ⋅ 1) = f(4)

k ⋅ 1 = 4

k = 4

Answer 2

`k=4`

Explanation:

So we have the graphs of f(x) and g(x).

And we know that g(x) is defined as f(kx), where k is some constant.

First, from the graph we can note two points:

For g(x), we have the point (1,10) and for f(x), we have the point (4,10).

In other words:

`g(1)=10`

And since we know the g(x) is f(kx), this means that:

`g(1)=10\\g(1)=10=f(1(k))=10`

And we know the for f(x) to be 10, the initial value is 4. Therefore:

`f(1(k))=10=f(4)\\1k=4\\k=4`

Therefore, the value of k is 4.