A change is applied to f x to give a new function g 2 x . This change is defined as g 2 x = 1 2 f x . Write down the coordinates of the eight points of g 2 x . Draw and label the graph of g 2 x on the same coordinate plane as f x .

According to the question, A change is applied to f x to give a new function g 2 x . This change is defined as g 2 x = 1 2 f x . Let f x = x 2 Given that, g 2 x = 1 2 f x Then, g 2 x = 1 2 x 2 The coordinates of the eight points of g 2 x are 1 , 0 . 5 , - 1 , 0 . 5 , 2 , 2 , - 2 , 2 , 3 , 4 . 5 , - 3 , 4 . 5 , 4 , 8 and 0 , 0 And the coordinates of the eight points of f x are 1 , 1 , - 1 , 1 , 2 , 4 , - 2 , 4 , 3 , 9 , - 3 , 9 , 4 , 16 and 0 , 0

EASY

MYP:4-5

IMPORTANT

Earn 100

The graph of $y = x^{2}$ is translated in the $x$ -direction and then reflected in the $x$ -axis to give curve $C$ . Find the equation of curve $C$ .

Important Questions on Function Transformations

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 1

Draw a coordinate plane with axes from $- 10$ to $10$ .

Plot, these points: $(- 4, - 5), (- 3, - 2), (- 2, 0), (- 1, 1), (0, 0), (1, - 1), (4, 1) and (5, 3)$ .

This set of eight points defines the function $f (x)$ . Join the points with a smooth curve.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 2

A change is applied to $f (x)$ to give a new function $g_{1} (x)$ . This change is defined as $g_{1} (x) = 2 f (x)$ .

Write down the coordinates of the eight points of $g_{1} (x)$ .

HARD

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 2

A change is applied to $f (x)$ to give a new function $g_{1} (x)$ . This change is defined as $g_{1} (x) = 2 f (x)$ .

Write down the coordinates of the eight points of $g_{1} (x)$ .

Draw and label the graph of $g_{1} (x)$ on the same coordinate plane as $f (x)$ .

HARD

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 3

A change is applied to $f (x)$ to give a new function $g_{2} (x)$ . This change is defined as $g_{2} (x) = \frac{1}{2} f (x)$ .

Write down the coordinates of the eight points of $g_{2} (x)$ .

Draw and label the graph of $g_{2} (x)$ on the same coordinate plane as $f (x)$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 4

Make a generalization for what happens when the function $f (x)$ changes to $g (x) = a f (x)$ , when $0 < a < 1$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 4

Make a generalization for what happens when the function $f (x)$ changes to $g (x) = a f (x)$ , when $a > 1$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 5

Draw the graph of $f (x)$ again on a new coordinate plane. A change is applied to $f (x)$ to give a new function $h (x)$ . This change is defined as $h (x) = f (2 x)$ .

Write down the coordinates of the eight points of $h (x)$ , for example the point $(- 4, - 5)$ will become $(- 2, - 5)$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 4 - Function Transformations>Exploration 4>Q 5

Draw the graph of $f (x)$ again on a new coordinate plane. A change is applied to $f (x)$ to give a new function $h (x)$ . This change is defined as $h (x) = f (2 x)$ .

Draw and label the graph of $h (x)$ on the same coordinate plane as $f (x)$ .

The graph of y=x2 is translated in the x -direction and then reflected in the x -axis to give curve C. Find the equation of curve C.

Important Questions on Function Transformations

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The graph of $y = x^{2}$ is translated in the $x$ -direction and then reflected in the $x$ -axis to give curve $C$ . Find the equation of curve $C$ .