Question

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

Answer 1

Answer:

k=2

Step-by-step explanation:

Clearly both the functions are straight lines

the equation of  straight line passing through the two points (a , b) and (c , d) is $y-b=\frac{d-b}{c-a}(x-a)$

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

the equation is $y-0=\frac{4-0}{0-(-4)}(x-(-4))$

y=x+4

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

the equation is $y-0=\frac{4-0}{0-(-2)}(x-(-2))$

y=2x+4

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

clearly g(x)=f(2x)

therefore k=2