Write down the equation of the function corresponding to the graph

[mathlearn]

Data

A graph in the form of $y=(x-1)^2-6$

Problem

Write down the equation of the function corresponding to the graph obtained when the above graph is translated 1 unit in the negative direction of the $x$ axis

Workings:

-

Where do I need help

In writing the equation of the funtion.

 

[MarkFL]

If we are given a function $f(x)$, then to translate the graph of that function $k$ units to the left, we may use $f(x+k)$.

Can you proceed?

 

[mathlearn]

If we are given a function $f(x)$, then to translate the graph of that function $k$ units to the left, we may use $f(x+k)$.

Can you proceed?

$\displaystyle f(x)=a(x-h)^2+k$

The function is in this form.

Substituting the values,

$y=(x-1)^2-6$

k=-6

Is it $f(x-6)$? but I am not sure whether this is correct?

 

[MarkFL]

You are given:

\(\displaystyle y(x)=(x-1)^2-6\)

So, to translate this one unit to the left, use:

\(\displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6\)

 

[mathlearn]

You are given:

\(\displaystyle y(x)=(x-1)^2-6\)

So, to translate this one unit to the left, use:

\(\displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6\)

Thank you very much (Yes) , Now I see it in desmos

[graph]rqbf6pohnc[/graph]

If we are given a function $f(x)$, then to translate the graph of that function $k$ units to the left, we may use $f(x+k)$.

Can you proceed?

But what I don't still understand is it's derivation.

Now what has actually happened here \(\displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6\);

Using $f(x+k)$ Do you plug in the values for $f,x,k$ from the given function.

What does $f$ stand for & from which part of the function was a value taken.

A comment here would be highly appreciated :)

 

[MarkFL]

Suppose we are given a function $f(x)$ and we wish to shift the graph of that function horizontally. If we wish to shift the function to the left $k$ units, then we can think of accomplishing this by moving our coordinate axes horizontally to the right $k$ units, that is:

\(\displaystyle X=x+k\)

So now what we have is that:

\(\displaystyle f(X)=f(x+k)\)

is the graph of $f(x)$ shifted to the left by $k$ units. Now, in this problem, we are given the function:

\(\displaystyle y(x)=(x-1)^2-6\)

And we are told to shift it 1 unit to the left.

So, in terms of what I posted above, we have $y=f,\,k=1$ and so there results:

\(\displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6\)

 

[mathlearn]

Suppose we are given a function $f(x)$ and we wish to shift the graph of that function horizontally. If we wish to shift the function to the left $k$ units, then we can think of accomplishing this by moving our coordinate axes horizontally to the right $k$ units, that is:

\(\displaystyle X=x+k\)

So now what we have is that:

\(\displaystyle f(X)=f(x+k)\)

is the graph of $f(x)$ shifted to the left by $k$ units. Now, in this problem, we are given the function:

\(\displaystyle y(x)=(x-1)^2-6\)

And we are told to shift it 1 unit to the left.

So, in terms of what I posted above, we have $y=f,\,k=1$ and so there results:

\(\displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6\)

(Yes) Thank you very much again

To shift the function to the left y(x+1) and vice versa to shift the function right y(x-1)