MYP Extended Mathematics Topic Horizontal Translation Revision Notes

MYP Extended Mathematics Topic Horizontal Translation Revision Notes | RevisionDojo

Horizontal transformations change a graph by altering the input (the $x$-values) of a function.
Because the change happens inside the function, horizontal transformations often feel "backwards" at first, especially translations.

Horizontal Translations Move Graphs Left Or Right

A horizontal translation shifts a graph left or right.

Definition

Horizontal translation

A transformation that moves the graph of $y=f(x)$ left or right by changing the input to $f$.

The Key Rules For $f(x-h)$ And $f(x+h)$

Right shift by $h$: $y=f(x-h)$ (when $h>0$)
Left shift by $h$: $y=f(x+h)$ (when $h>0$)

So, the sign inside the bracket is the opposite of the direction you move.

Common Mistake

A common mistake is to think $f(x-h)$ moves left because of the minus sign.
It actually moves the graph right by $h$.

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Tip

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Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

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Horizontal transformations change a graph by altering the input (the $x$-values) of a function.
Because the change happens inside the function, horizontal transformations often feel "backwards" at first, especially translations.

Horizontal Translations Move Graphs Left Or Right

A horizontal translation shifts a graph left or right.

Definition

Horizontal translation

A transformation that moves the graph of $y=f(x)$ left or right by changing the input to $f$.

The Key Rules For $f(x-h)$ And $f(x+h)$

Right shift by $h$: $y=f(x-h)$ (when $h>0$)
Left shift by $h$: $y=f(x+h)$ (when $h>0$)

So, the sign inside the bracket is the opposite of the direction you move.

Common Mistake

A common mistake is to think $f(x-h)$ moves left because of the minus sign.
It actually moves the graph right by $h$.

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Advanced Number and Bounds3 subtopics

Inequalities and Modelling1 subtopic

Function Transformations4 subtopics

Advanced Probability1 subtopic

Geometric Transformations1 subtopic

Variation and Standard Deviation3 subtopics

Trigonometric Functions and Rules4 subtopics

Sequences, Rational Expressions and Equations5 subtopics

Covariance and Correlation3 subtopics

Logarithms and Non-Linear Inequalities3 subtopics

Graph Theory and Vectors4 subtopics

MYP Extended Mathematics Horizontal Translation Notes

Advanced Number and Bounds3 subtopics

Inequalities and Modelling1 subtopic

Function Transformations4 subtopics

Advanced Probability1 subtopic

Geometric Transformations1 subtopic

Variation and Standard Deviation3 subtopics

Trigonometric Functions and Rules4 subtopics

Sequences, Rational Expressions and Equations5 subtopics

Covariance and Correlation3 subtopics

Logarithms and Non-Linear Inequalities3 subtopics

Graph Theory and Vectors4 subtopics

Horizontal Translations Move Graphs Left Or Right

The Key Rules For $f(x-h)$ And $f(x+h)$

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Horizontal Translations Move Graphs Left Or Right

The Key Rules For $f(x-h)$ And $f(x+h)$

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account