Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value. two parabolas open up with f of x passing through 8 comma 6 and g of x passing through 2 comma 6 k = −4 k = negative one fourth k = one fourth k = 4

Here we have a problem of transformations, particularly, horizontal dilations.

We will find that the correct option is k = 4.

We have two functions:

f(x) and g(x) = f(k*x)

We know that:

f(x) passes through the point (8, 6)

This means that:

f(8) = 6

And we know that g(x) passes through (2, 6)

this means that:

g(2) = 6

Using these two and the representation of g(x), we can see that:

g(2) = f(k2) = 6

and we knew that f(8) = 6

then

k2 = 8

k = 8/2 = 4

Then the value of k is 4.

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