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Sagot :
First we notice that the vertex of the parabola is shift one unit to the left and three units down. To begin we need to remember the following rules:
Suppose c>0. To obtain the graph of
y=f(x)+c, shift the graph of f(x) a distance c units upwards.
y=f(x)-c, shift the graph of f(x) a distance c units downward.
y=f(x-c), shift the graph of f(x) a distance c units to the right.
y=f(x+c), shift the graph of f(x) a distance c units to the left.
Once we have this rules and knowing that the vertex move like we mentioned before we have that the new function should be of the form:
[tex]f(x+1)-3[/tex]From the graph we also notice that the function g is stretch by a factor of two, remembering the rule for stretching graphs:
If c>1 then the function y=f(x/c), stretch the graph of f(x) horizontally by a factor of c.
With this we conclude that the function g has to be of the form:
[tex]f(\frac{x}{2}+1)-3[/tex]Finally, we notice that the function f is:
[tex]f(x)=x^2[/tex]Threfore,
[tex]g(x)=(\frac{x}{2}+1)^2-3[/tex]then the answer is A.
HAve a nice day !
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