Solve the vertical stretch/compression graph problem

[chwala]

Homework Statement

see attached

Relevant Equations

Vertical stretch/compression knowledge

This is the problem,

Let $y=f(x)= (x-2)^2$. The graph of $y=af(x)$can be obtained from the graph of $y=f(x)$ by a stretch parallel to the y- axis with scale factor $a$. In our case here, $a=3$, therefore the corresponding graph is as indicated in blue. Find my graph below using desmos.

 

[DrClaude]

You can check what the value of $f(1)$ is.

 

[chwala]

$f(1) =1$, therefore $af(1)=3f(1)= 3⋅1 =3$
From$f(x)$ to $af(x)$, the scale factor is $k=3$

 

[DrClaude]

$f(1) =1$, therefore $af(1)=3f(1)= 3.1 =3$

So indeed, the correct graph is the second one.

From$f(x)$ to $af(x)$, the scale factor is $k=3$

That's correct, but I don't see how this is related to the question of finding the correct graph.

 

[chwala]

True, not related mate...cheers

So indeed, the correct graph is the second one.That's correct, but I don't see how this is related to the question of finding the correct graph.

 

[SammyS]

$f(1) =1$, therefore $af(1)=3f(1)= 3.1 =3$
From$f(x)$ to $af(x)$, the scale factor is $k=3$

You may want to write $3 \!\cdot \!\!1$ as
##3 \cdot 1 ##
rather than as
##3.1## .

 

[chwala]

You may want to write $3 \!\cdot \!\!1$ as
##3 \cdot 1 ##
rather than as
##3.1## .

Yes Sammy...actually I didn't forget, it is only that my android phone wasn't opening the tabs related to signs...i will for sure have that fixed.