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Alina [70]
3 years ago
8

The graph of f(x) = x2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describ

es g(x)?
g(x) = (x + 3)2
g(x) = x2 − 3
g(x) = x2 + 3
g(x) = (x − 3)2

Mathematics
1 answer:
ANTONII [103]3 years ago
6 0

Answer:

g(x) = (x + 3)^2

Step-by-step explanation:

When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.

If we have a quadratic function

f(x)=x^2

and the graph is shifted 3 units to the left, then we can think of a new unit u that is:

g(x)=u^2

The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.

Then, the relation between u and x is:

u-x=0-(-3)=3\\\\u=x+3

We can use this relation in the new graph and replace u as:

g(x)=(x+3)^2

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