# Thread: Horizontal And Vertical Translations

1. ## Horizontal And Vertical Translations

When you alter a graph, you transform it. If you transform a graph without changing its shape, you translate it. Vertical and horizontal transformations are translations. When y = f(x) + d, shift (translate) the graph of y = f(x) vertically (upward if d > 0, downward if d < 0).

Example: 1. Problem: Translate y = x2 upward by 1. Solution: You have been asked to shift the graph upward 1. Rewrite the equation to do this, and then graph. y = x2 + 1 The figure below is a graph of the solution.

When y = f(x + c), translate the graph of y = f(x) horizontally (left if c > 0, right if c < 0).

Example: 2. Problem: Sketch the graph of y = |x + 2|. Solution: First, graph y = |x|, then shift it to the left 2 places. The figure below is a graph of the solution.

I saw this online and i was wondering how can you tell if it's a Horizontal Translation or Vertical one? If so, what are usually these translation used for?

2. Suppose you have a function $y=f(x).$ Vertical translations look like $y=f(x)\pm c$: they correspond to a shifting of the range of a function, or its output. Horizontal translations look like $y=f(x\pm c)$: they correspond to a shifting of the domain of a function, or its input.

There are a few functions where you can't tell the difference between the two translations: straight lines, for example: $y=x+c$ could be viewed either way. Or, if you had a slope of $2,$ then the line $y=2x+4$ could have a positive vertical translation of $4$ from the line $y=2x$, or it could be viewed as $y=2(x+2),$ in which case it's a horizontal translation of $2$ to the left.

I'll give you one application of translations: modeling switches in electrical circuits. The Heaviside step function is defined as

$u(x)=\begin{cases}1&x\ge 0\\0&x<0\end{cases}.$

I can think of a switch turning on when I start a clock timer at $t=0$ as the function $u(t)$. But now, suppose I want to flip a switch for one second, and then switch it back off? I could model that as a horizontally translated difference of step functions: $u(t)-u(t-1).$ We might want to model that if we're trying to solve the differential equation governing the behavior of the circuit.

3. Thank you very much and it was detailed =D

4. You're welcome. Have a good one!

,

,

,

# a horizontal translation differ

Click on a term to search for related topics.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://mathhelpforum.com/pre-calculus/153387-horizontal-vertical-translations.html", "fetch_time": 1498693206000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2017-26/segments/1498128323807.79/warc/CC-MAIN-20170628222452-20170629002452-00453.warc.gz", "warc_record_offset": 240625012, "warc_record_length": 11087, "token_count": 629, "char_count": 2428, "score": 4.25, "int_score": 4, "crawl": "CC-MAIN-2017-26", "snapshot_type": "longest", "language": "en", "language_score": 0.8899548649787903, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00012-of-00064.parquet"}