$What can we say about the transformation ?$

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$What can we say about the transformation ?$

f(x) = x^3 + x^2 - 14x - 24
So f(x) = (x+2)*(x+3)*(x-4)

The transformation that i need to explain is :
f_1 = f(x+a)
So f_1 = (x+2+a)*(x+3+a)*(x-4+a)

At my known, the whole function is equally moving on the x axis when the value of (a) changes. (0;0) points can be found when (a) = -2 , -3 or +4.
But beside that, i don’t know what to say… If you guys have anything more to add to it. I would gladly take the information.

Functions

Studenthere

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You are right. Given a function $f(x)$ and a real number $a>0$,

the graph of the function $f_1(x)=f(x+a)$ is the same as the graph of the function $f(x)$ but shifted $a$ unites to the left.
the graph of the function $f_2(x)=f(x-a)$ is the same as the graph of the function $f(x)$ but shifted $a$ unites to the right.

So the sign of $a$ determines if the graph is shifted to the right or left. This is pretty much all one can say about shifing the graph of a funciton to left or right.

Also given a function $f(x)$ and $a>0$, the graph of the function $g(x)=f(x)+a$ is the same as the graph of the function $f(x)$ but shifted $a$ unites up. Similarly, the graph of the function $g(x)=f(x)-a$ is the same as the graph of the function $f(x)$ but shifted $a$ unites down.

Erdos

Erdos

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Please let me know if you have any other questions or need any clarifications.

$What can we say about the transformation ?$

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