Draw the graph of f ( x ) = x 2 . Draw the graphs of g ( x ) = f ( 1 2 x ) and h ( x ) = f ( 2 x ) on the same axes.

Given that f ( x ) = x 2 . x - 2 - 1 0 1 2 f ( x ) = x 2 4 1 0 1 4 y = f ( a x ) is a horizontal dilation of f ( x ) , scale factor 1 a , parallel to x -axis where a > 0 . g ( x ) = f ( 1 2 x ) = 1 4 x 2 is a horizontal dilation of f ( x ) with the scale factor 2 , parallel to x -axis. ( 0 , 0 ) on f ( x ) = x 2 is moved to ( 0 , 0 ) on g ( x ) = f ( 1 2 x ) ( 1 , 1 ) on f ( x ) = x 2 is moved to ( 1 , 1 4 ) on g ( x ) = f ( 1 2 x ) ( - 1 , 1 ) on f ( x ) = x 2 is moved to ( - 1 , 1 4 ) on g ( x ) = f ( 1 2 x ) . So, h ( x ) = f ( 2 x ) is a horizontal dilation of f ( x ) with scale factor 1 2 , parallel to x -axis ( 0 , 0 ) on f ( x ) = x 2 is moved to ( 0 , 0 ) on h ( x ) = f ( 2 x ) ( 1 , 1 ) on f ( x ) = x 2 is moved to ( 1 , 4 ) on g ( x ) = f ( 2 x ) ( - 1 , 1 ) on f ( x ) = x 2 is moved to ( - 1 , 4 ) on g ( x ) = f ( 2 x ) . So, h ( x ) = f ( 2 x ) is a horizontal dilation of f ( x ) with the scale factor 1 2 , parallel to x -axis. Thus, the graph of f ( x ) , g ( x ) and h ( x ) on the same axes are drawn below.

E M B I B E

MYP Mathematics A concept based approach 4&5 Standard>Chapter 20 - A Frog into a Prince (Transforming Functions)>Practice 4>Q 1

EASY

MYP:4-5

IMPORTANT

Earn 100

Copy this sketch of $f (x) = {(x - 1)}^{2}$ . Sketch the graph of $g (x) = 2 f (x)$ on the same axes.

Important Questions on A Frog into a Prince (Transforming Functions)

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 20 - A Frog into a Prince (Transforming Functions)>Practice 4>Q 2

Copy this sketch of $f (x) = - x^{2} + 4$ . Sketch the graph of $h (x) = f (2 x)$ on the same axes.

Question Image

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 20 - A Frog into a Prince (Transforming Functions)>Practice 4>Q 3

Copy this sketch of $f (x) = x^{2} + 2 x - 3$ . Sketch the graph of $g (x) = f (3 x)$ on the same axes. Sketch the graph of $h (x) = - f (3 x)$ on the same axes.