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animegirl02
12.12.2020 •
Mathematics
Which statements describe transformations performed in f (x) = x^2 to create g (x) = 2x^2 + 5? select all that apply.
a. a vertical stretch with a scale factor of .5
b. a translation of 5 units to the right.
c. a translation of 5 units up.
d. a vertical stretch with a scale factor of 2.
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Ответ:
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) + kLet 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 upa vertical stretch with a scale factor of 2Ответ:
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