Question

Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.

Two lines labeled f of x and g of x. Line f of x passes through points negative 6, negative 2 and negative 3, 1. Line g of x passes through points negative 2, negative 2 and negative 1, 1.

−3
negative one third
one third
3

Answer 1

The value of k is 3.

Explanation:

The function f(x) passes through the points (0,4) and (-6,-2)

So the equation of the function is
`(y-4)/(4-(-2)) = (x-0)/(0-(-6))`

⇒ y = x + 4 ....... (1)

Again the function g(x) passes through the points (0,4) and (-2,-2).

Therefore, the equation of g(x) will be
`(y-4)/(4-(-2)) =(x-0)/(0-(-2))`

⇒ y = 3x + 4

Therefore, g(x) = 3x + 4 = f(3x) {from equation (1).

So, the value of k is 3. (Answer)