Question

Given f(×) and g(×) = f(kx), use the graph to determine the value of k

Answer 1

The value of k is 3

Solution:

Let us first find the equation of the line f(x).

The points on the line are (-6, -2) and (0, 4).

Here, $x_1=-6, y_1=-2, x_2=0, y_2=4$

Formula to find equation of a line:

$\frac{y-y_1}{x-x_1} =\frac{y_2-y_1}{x_2-x_1}$

$\frac{y-(-2)}{x-(-6)} =\frac{4-(-2)}{0-(-6)}$

$\frac{y+2}{x+6} =\frac{4+2}{6}$

$\frac{y+2}{x+6} =\frac{1}{1}$

Do cross multiplication.

y + 2 = x + 6

y = x + 4

f(x) = x + 4

Given that g(x) = f(kx)

g(x) = kx + 4

The point in the graph of g(x) is ( -2, -2).

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

we know that g(-2) = -2.

-2 = -2k + 4

Subtract 4 from both sides.

-6 = -2k

Divide by -2 on both sides.

3 = k

k = 3

The value of k is 3.