Note: x-intercepts

[mathdad]

h(x) = (x + 2)( x - 4)^3

A. Identify the x-intercepts of the graph of h.

B. What are the x-intercepts of the graph of y = h(x - 2)?

NOTE: I seek solution steps for parts A and B. I want to try this on my own (following your steps) before posting my work here. Good day everyone.

 

[MarkFL]

A. I assume you can already do this part.

B. How will the graph of \(h\) be shifted here?

 

[MarkFL]

To follow up:

The \(x\)-intercepts are:

[MATH](-2,0),\,(4,0)[/MATH]
The graph of \(h(x-2)\) will be the graph of \(h(x)\) shifted 2 units to the right, hence the \(x\)-intercepts will be:

[MATH](0,0),\,(6,0)[/MATH]

 

[mathdad]

To follow up:

The \(x\)-intercepts are:

[MATH](-2,0),\,(4,0)[/MATH]
The graph of \(h(x-2)\) will be the graph of \(h(x)\) shifted 2 units to the right, hence the \(x\)-intercepts will be:

[MATH](0,0),\,(6,0)[/MATH]

Part A is easy. Let x = 0 to find the y-intercepts and y = 0 to find the x-intercepts.
For part B, you said shift h(x) two units to the right. What about (x - 4)^3? Does (x - 4) indicate to make another shift movement of the given function?

 

[Deleted member 4993]

Part A is easy. Let x = 0 to find the y-intercepts and y = 0 to find the x-intercepts.
For part B, you said shift h(x) two units to the right. What about (x - 4)^3? Does (x - 4) indicate to make another shift movement of the given function?

"Does (x - 4) indicate to make another shift movement of the given function"

No - read the second part of the question carefully!

What is it asking you to do?

Now read MarkFL's response again!

Now think... then write the answer to the question (What is it asking you to do?) with a paper and pencil

Now read MarkFL's response again!

Now ask questions.....

 

[mathdad]

"Does (x - 4) indicate to make another shift movement of the given function"

No - read the second part of the question carefully!

What is it asking you to do?

Now read MarkFL's response again!

Now think... then write the answer to the question (What is it asking you to do?) with a paper and pencil

Now read MarkFL's response again!

Now ask questions.....

I got this question mixed up with another recently posted. This is where the confusion stems from.

 

[Otis]

I got this question mixed up with another recently posted ...

Are you sure?

h(x) = (x + 2)( x - 4)^3

... graph of y = h(x - 2) ...

... What about (x - 4)^3? Does (x - 4) indicate to make another shift ...?

A horizontal shift happens when a function's inputs are all changed by the same amount.

The expression x - 4 is not an input, so it does not represent a shift. The binomial x-4 is a factor of the polynomial which defines function h(x).

The inputs for function h(x) are not the same as they are for function h(x-2). Those are two different functions.

We define the new (shifted) function like this:

h(x - 2) = ([x-2] + 2)*([x-2] - 4)^3

We could simplify, by assigning new names for both the new function and its input variable. Let t=x-2.

g(t) = (t)(t - 6)^3

We see that new function g has t-intercepts 0 and 6.

\(\;\)