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
-1/2
1/2
2

Answer 1

Answer:

1/2

Step-by-step explanation:

Answer 2

Answer:

k=2

Step-by-step explanation:

We are given that

Line of f(x) passes through the points (-4,0) and (0,4).

Line of g(x) pass through the points (-2,0) and (0,4).

$g(x)=f(k\cdot x)$

We have to determine the value of k.

$f(-4)=0$

$g(-2)=0$

slope of f(x)=$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0+4}=1$

Equation of f(x) which is passing through the point (-4,0) with slope 1

$y-0=1(x+4)$

By using slope-point form:$y-y_1=m(x-x_1)$

$y=x+4$

$g(x)=f(kx)$

Replace x by kx

Equation of g(x)

$y=kx+4$

Substitute x=-2

$g(-2)=-2k+4$

$-2k+4=0$

$2k=4$

$k=\frac{4}{2}=2$

Hence, the value of $k=2$