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Suppose f(x) = x2. What is the graph of g(x) = f(3x)?

Help Suppose Fx X2 What Is The Graph Of Gx F3x class=

Sagot :

absor201

Answer:

we conclude that g(x) = 9x² is the result of f(x) vertically stretched by multiplying each of its y-coordinates by 9.

Also, check the attached graph is matched with option B.

Hence, option (B) is the correct graph.

Step-by-step explanation:

Given

  • f(x) = x²
  • g(x) = f(3x)

so

  • g(x) = (3x)² = 9x²

Thus, the graph of g(x) = 9x² is shown below.

From the graph, it is clear that at x = 0, y = 0

So, the y-intercept is at (0, 0).

Clearly

  • f(x) = x²
  • g(x) = 9x²

Note that the vertex of the graph also lies at (0, 0), because it is clear that g(x) = 9x² is the result of f(x) vertically stretched by multiplying each of its y-coordinates by 9.

Since 9 > 0, it means g(x) = 9x² is vertically stretched by multiplying each of its y-coordinates by 9.

Therefore, we conclude that g(x) = 9x² is the result of f(x) vertically stretched by multiplying each of its y-coordinates by 9.

Also, check the attached graph is matched with option B.

Hence, option (B) is the correct graph.

View image absor201
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