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Given f(x) = |x|, what would be the function rule for a vertical stretching of f(x) by scale factor 7?

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Final answer:

The function rule for a vertical stretching of f(x) = |x| by a scale factor of 7 is g(x) = 7|x|. This operation multiplies each y-value by 7, causing the V-shaped graph of the absolute value function to become taller while keeping its vertex at the origin.

Step-by-step explanation:

To determine the function rule for a vertical stretching of the function f(x) = |x| by a scale factor of 7, you multiply the original function by 7 to scale the values appropriately. Hence, the new function after the stretch is expressed as g(x) = 7|x|. Vertical stretching of a graph means that each y-coordinate is multiplied by the scale factor, causing the graph to stretch away from the x-axis if the scale factor is greater than 1, or to compress towards the x-axis if it is between 0 and 1.

The absolute value function f(x) = |x| has a V-shape with its vertex at the origin (0,0). When applying the vertical stretch by a factor of 7, this V-shape becomes taller and narrower while maintaining the overall shape and symmetry. The vertex remains at the origin, but now each point on f(x) is seven times further from the x-axis. Therefore, the point (1, 1) on f(x) becomes (1, 7) on g(x), and similarly, the point (-1, 1) on f(x) becomes (-1, 7) on g(x). This expanded shape is still symmetric about the y-axis, maintaining the property of the original absolute value function being an even function.

User Ketan Ramteke
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Answer:

Step-by-step explanation:

For a vertical stretching of
f(x)=∣x∣ by a scale factor of 7, the rule for the stretched function
g(x) would be:
g(x)=7⋅∣x∣

In this case, you multiply the absolute value function
∣x∣ by the scale factor (7) to achieve the vertical stretching.

User Tersakyan
by
8.2k points

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