Question 1(Multiple Choice Worth 1 points)
(02.05 MC)

Given f(x) and g(x) = k⋅f(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 negative 2, 2. Line g of x passes through points negative 4, 0 and negative 2, negative 10.

A) −5
B) - 1/5
C) 1/5
D) 5

If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k.
If 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k
If k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.

∵ g(x) = k f(x)

∴ g(x) is the image of f(x) after vertical stretched or compressed by

scale factor of k

∴ The y-coordinates of each point on f(x) will multiply by k

From the graph:

∵ f(x) is represented by a line passes through points (-4 , 0)

and (-2 , 2)

∵ g(x) is represented by a line passes through points (-4 , 0)

and (-2 , -10)

∵ The image of point (-4 , 0) on f(x) = (-4 , 0 × k)

∵ 0 × k = 0

∴ The image of point (-4 , 0) on f(x) = (-4 , 0) on g(x)

∵ The image of point (-2 , 2) on f(x) = (-2 , 2 × k)

∴ The image of point (-2 , 2) on f(x) = (-2 , 2 k)

∵ The image of point (-2 , 2) on f(x) = (-2 , -10) on g(x)

∴ (-2 , 2 k) = (-2 , -10)

- Equate the y-coordinates

∴ 2 k = -10

- Divide both sides by 2

∴ k = -5

By using the graph the value of k is -5

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You can learn more about transformation in brainly.com/question/2415963

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