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Pavlova-9 [17]
3 years ago
11

Which statements describe transformations performed in f (x) = x^2 to create g (x) = 2x^2 + 5? select all that apply.

Mathematics
1 answer:
snow_tiger [21]3 years ago
8 0

Answer:

The statements describe transformations performed in f(x) to create g(x) are:

a translation of 5 units up ⇒ c

a vertical stretch with a scale factor of 2 ⇒ d

Step-by-step explanation:

  • If f(x) stretched vertically by a scale factor m, then its image g(x) = m·f(x)
  • If f(x) translated vertically k units, then its image h(x) = f(x) + k

Let us use these rule to solve the question

∵ f(x) = x²

∵ g(x) is created from f(x) by some transformation

∵ g(x) = 2x² + 5

→ Substitute x² by f(x) in g(x)

∴ g(x) = 2f(x) + 5

→ Compare it with the rules above

∴ m = 2 and k = 5

→ That means f(x) is stretched vertically and translated up

∴ f(x) is stretched vertically by scal factor 2

∴ f(x) is translated 5 uints up

The statements describe transformations performed in f(x) to create g(x) are:

  • a translation of 5 units up
  • a vertical stretch with a scale factor of 2
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