Question

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 1

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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