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Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.


Graph of two lines. f of x passes through 2, 0 and 3, 2, and g of x passes through two thirds, 0 and 1, 2.


3

one third

negative one third

−3

Answer :

UPENDOGO

f(x)

(2, 0) and (3, 2)

m = y - y1

x - x1

m = 2 - 0

3 - 2

m = 2

y - y1 = m(x - x1)

y - 0 = 2(x - 2)

y = 2x - 4

f(x) = 2x - 4

g(x)

(2/3, 0) and (1, 2)

m = y - y1

x - x1

m = 2 - 0

1 - 2/3

m = 6

y - y1 = m(x - x1)

y - 2 = 6(x - 1)

y = 6x - 4

g(x) = 6x - 4

since both equations are linear that means the graphs will be straight lines with y-intercept being -4 for both of the graphs.

if,

g(x) = f(k*x)

f(x) = 2x - 4

f(k*x) = 2k*x - 4

6x - 4 = 2k*x - 4

6x = 2kx

6 = 2k

k = 3.

I hope the answer is correct. All the best!

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