### Transformations of functions

Question Sample Titled 'Transformations of functions'

Transformation of the graphTransformation of the function
Translate upwards ${k}$ units${f{{\left({x}\right)}}}+{k}$
Translate downwards ${k}$ units${f{{\left({x}\right)}}}-{k}$
Translate leftwards ${k}$ units${f{{\left({x}+{k}\right)}}}$
Translate rightwards ${k}$ units${f{{\left({x}-{k}\right)}}}$
Reflect ${x}$ the x-axis$-{f{{\left({x}\right)}}}$
Reflect ${y}$ the y-axis${f{{\left(-{x}\right)}}}$
Enlarge along the ${y}$ axis to ${k}$ times the original, where ${k}\gt{1}$${k}{f{{\left({x}\right)}}}$
Reduce along the ${y}$ axis to ${k}$ times the original, where ${0}\lt{k}\lt{1}$
Enlarge along the ${x}$ axis to $\dfrac{{1}}{{k}}$ times the original, where ${0}\lt{k}\lt{1}$${f{{\left({k}{x}\right)}}}$
Reduce along the ${x}$ axis to $\dfrac{{1}}{{k}}$ times the original, where ${k}\gt{1}$

 Example In each of the following, if ${f{{\left({x}\right)}}}={\left({x}-{1}\right)}^{{2}}$ is transformed to ${g{{\left({x}\right)}}}$ , describe the corresponding transformations on the graph of ${y}={f{{\left({x}\right)}}}$ .

 (a) ${g{{\left({x}\right)}}}={\left({x}+{1}\right)}^{{2}}$ (b) ${g{{\left({x}\right)}}}=-{\left({x}-{1}\right)}^{{2}}$ (c) ${g{{\left({x}\right)}}}={2}{\left({x}-{1}\right)}^{{2}}$

 Solution (a) ∵  ${g{{\left({x}\right)}}}={\left[{\left({x}+{2}\right)}-{1}\right]}^{{2}}={f{{\left({x}+{2}\right)}}}$ ∴   The graph of ${y}={g{{\left({x}\right)}}}$ is obtained by translating the graph of ${y}={f{{\left({x}\right)}}}$ leftwards by ${2}$ units. (b) ∵  ${g{{\left({x}\right)}}}=-{\left({x}-{1}\right)}^{{2}}=-{f{{\left({x}\right)}}}$ ∴   The graph of ${y}={g{{\left({x}\right)}}}$ is obtained by reflecting the graph of ${y}={f{{\left({x}\right)}}}$ about the ${x}$ axis. (c) ∵  ${g{{\left({x}\right)}}}={2}{\left({x}-{1}\right)}^{{2}}={2}{f{{\left({x}\right)}}}$ ∴   The graph of ${y}={g{{\left({x}\right)}}}$ is obtained by enlarging the graph of ${y}={f{{\left({x}\right)}}}$ along the ${y}$ axis to ${2}$ times the original.

*聲明：此資源並不屬於 ePractice ，僅屬外部資源建議。ePractice 不就其內容負責亦不收受其產生的任何收益。

*聲明：此資源並不屬於 ePractice ，僅屬外部資源建議。ePractice 不就其內容負責亦不收受其產生的任何收益。

# 專業備試計劃

Premium DSE Preparation Plan

Level 4+ 保證及 5** 獎賞

ePractice 會以電郵、Whatsapp 及電話提醒練習

ePractice 會定期提供溫習建議

Level 5** 獎勵：會員如在 DSE 取得數學 Level 5** ，將獲贈一套飛往英國、美國或者加拿大的來回機票，唯會員須在最少 180 日內每天在平台上答對 3 題 MCQ。

Level 4 以下賠償：會員如在 DSE 未能達到數學 Level 4 ，我們將會全額退回所有會費，唯會員須在最少 180 日內每天在平台上答對 3 題 MCQ。

# FAQ

ePractice 是甚麼？

ePractice 是一個專為中四至中六而設的網站應用程式，旨為協助學生高效地預備 DSE 數學（必修部分）考試。由於 ePractice 是網站應用程式，因此無論使用任何裝置、平台，都可以在瀏覽器開啟使用。更多詳情請到簡介頁面。

ePractice 可以取代傳統補習嗎？

1. 會員服務期少於兩個月；或
2. 交易額少於 HK\$100。

Initiating...

HKDSE 數學試題練習平台