By using the graph the value of k is -5 ⇒ answer A
Step-by-step explanation:
Let us revise some transformation
A vertical stretching is the stretching of the graph away from the x-axis
A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis.
- 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
Learn more:
You can learn more about transformation in brainly.com/question/2415963
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