The graph of f(x) = 4x2 is shifted 5 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)? a g(x) = 4x2 + 5 b g(x) = 4(x − 5)2 c g(x) = 4x2 − 5 d g(x) = 4(x + 5)2
The graph of f(x) = 4x2 is shifted 5 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)?
a
g(x) = 4x2 + 5
b
g(x) = 4(x − 5)2
c
g(x) = 4x2 − 5
d
g(x) = 4(x + 5)2
ANSWER:
The graph of f(x) = 4x^2 is shifted 5 units to the left to obtain the graph of g(x).
To shift a function 5 units to the left, we replace x with (x + 5) in the original function.
Comparing the options given:
a) g(x) = 4x^2 + 5
This equation represents a vertical shift upwards by 5 units, not a shift to the left.
b) g(x) = 4(x − 5)^2
This equation represents a shift to the right by 5 units, not a shift to the left.
c) g(x) = 4x^2 − 5
This equation represents a vertical shift downwards by 5 units, not a shift to the left.
d) g(x) = 4(x + 5)^2
This equation represents a shift to the left by 5 units, as required.
Therefore, the equation that best describes g(x) when the graph of f(x) = 4x^2 is shifted 5 units to the left is:
d) g(x) = 4(x + 5)^2
IMPORTANT:
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