Help with trigonometry Translations

[Lalala]

If the equation y=tanx is translated 3 units right and horizontally dilated by a scale factor of 1/4. What is the new equation. Is it y=tan(4x+3) or y=tan[4(x+3)].

The ”correct” answer is y=tan(4x+3) but I’m confused because in some cases the horizontal dilation is factored out.

 

[mario99]

I would say the answer is $y = \tan[ 4(x - 3) ]$

To illustrate the idea, consider the function $y = x^2$ and $y = ( 4[x - 3] )^2$

Graph the function and see what happens to the original graph.

 

[Dr.Peterson]

If the equation y=tanx is translated 3 units right and horizontally dilated by a scale factor of 1/4. What is the new equation. Is it y=tan(4x+3) or y=tan[4(x+3)].

The ”correct” answer is y=tan(4x+3) but I’m confused because in some cases the horizontal dilation is factored out.

Take it step by step:

Starting with $y=\tan(x)$, we translate it by replacing $x$ with $x-3$: $y=\tan(x-3)$.​

​

Now dilate it, by replacing $x$ with $4x$: $y=\tan(4x-3)$.​

​

So the "correct" answer is in fact correct. (And, yes, Mario is wrong.)​

When you do the dilation first and then shift (which is easier to visualize), you get the factored form, $y=\tan(4(x-3))$. But this is a different function!

See here:

Combining Function Transformations: Order Matters – The Math Doctors

www.themathdoctors.org

Function Transformations Revisited (I) – The Math Doctors

www.themathdoctors.org

Function Transformations Revisited (II) – The Math Doctors

www.themathdoctors.org

 

[mario99]

Take it step by step:

Starting with $y=\tan(x)$, we translate it by replacing $x$ with $x-3$: $y=\tan(x-3)$.​

​

Now dilate it, by replacing $x$ with $4x$: $y=\tan(4x-3)$.​

​

So the "correct" answer is in fact correct. (And, yes, Mario is wrong.)​

When you do the dilation first and then shift (which is easier to visualize), you get the factored form, $y=\tan(4(x-3))$. But this is a different function!

See here:

Combining Function Transformations: Order Matters – The Math Doctors

www.themathdoctors.org

Function Transformations Revisited (I) – The Math Doctors

www.themathdoctors.org

Function Transformations Revisited (II) – The Math Doctors

www.themathdoctors.org

I might be wrong, but non of the functions given by the OP is $y = \tan(4x - 3)$.

If the equation y=tanx is translated 3 units right and horizontally dilated by a scale factor of 1/4. What is the new equation. Is it y=tan(4x+3) or y=tan[4(x+3)].

The ”correct” answer is y=tan(4x+3) but I’m confused because in some cases the horizontal dilation is factored out.

I thought that this means we want our function to settle 3 steps on the right in the final state.

 

[Dr.Peterson]

I might be wrong, but non of the functions given by the OP is $y = \tan(4x - 3)$.

Yes, I failed to look closely at the signs, and focused only on the presence of parentheses, which was the focus of the question. We'll have to wait to hear back which part of what was said (the problem or the answers) was miscopied.

My guess at the moment is that the problem said to translate to the left, and that was copied wrong, perhaps because of all the "+" signs, which tend to make the mind think "right".

I thought that this means we want our function to settle 3 steps on the right in the final state.

We can only assume that (if the problem was reported correctly) it is intended to mean "in this order". If not, then it is not clearly stated, because order is an essential part of such a problem.

So, @Lalala, please show us the original problem exactly as stated, and the claimed answer exactly as given.

 

[mario99]

We can only assume that (if the problem was reported correctly) it is intended to mean "in this order". If not, then it is not clearly stated, because order is an essential part of such a problem.

So, @Lalala, please show us the original problem exactly as stated, and the claimed answer exactly as given.

If we have literally to follow the wording, then your explanation to ($y = \tan(4x-3)$) is correct. And I think that is what was intended by the question.