(02.02 LC) If g(x) = x2 – 4, find g(5)
2 answers:
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The rule of g(x) is g(x) = 2 + 4(x - 4) + 12
Step-by-step explanation:
Let us revise some transformation
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- 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
∵ f(x) = + 2x + 6
∵ The graph of f(x) is stretched vertically by a factor of 2
- That means the y-coordinate of each point on the graph is multiplied
by 2, then y = 2.f(x) as the 2nd rule above
∴ y = 2[ + 2x + 6]
∴ y = 2 + 4x + 12
∵ The graph of 2.f(x) is translated 4 units to the right
- That means substitute every x by (x - 4) as the 1st rule above
∴ g(x) = 2 + 4(x - 4) + 12
The rule of g(x) is g(x) = 2 + 4(x - 4) + 12
Learn more:
You can learn more about transformation in brainly.com/question/2451812
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