Question

the function g is a transformation of f. The grab below shows us as a solid blue line and g as a dotted red line. what is the formula of gA) g(x) =(x/2+1)²-3B) g(x) =(2x+1)²-3C) g(x) =(x/2-1)²-3D) g(x) =(x/2+1)²+3

Answer 1

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:

`f(x+1)-3`

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:

`f((x)/(2)+1)-3`

Finally, we notice that the function f is:

`f(x)=x^2`

Threfore,

`g(x)=((x)/(2)+1)^2-3`

then the answer is A.

HAve a nice day !