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 4, 0 and 0, 4. Line g of x passes through points negative 2, 0 and 0, 4.

-2
-1/5
1/5
2

Answer 1

k=2

Explanation:

Clearly both the functions are straight lines

the equation of straight line passing through the two points (a , b) and (c , d) is
`y-b=(d-b)/(c-a)(x-a)`

Now f(x) passes through (-4 , 0) and (0 , 4)

the equation is
`y-0=(4-0)/(0-(-4))(x-(-4))`

y=x+4

Now g(x) passes through (-2 , 0) and (0 , 4)

the equation is
`y-0=(4-0)/(0-(-2))(x-(-2))`

y=2x+4

here f(x)=x+4 and g(x)=2x+4

clearly g(x)=f(2x)

therefore k=2