(b) y = 2 x can be transformed to y = 2 x + 2 by a translation of 0 a . Find the value of a .

y = 2 x y = 2 x + 2 ( 1 ) . . . . . . . f ( x - a ) + b = 2 ( x - a ) + b = 2 x - 2 a + b ( 2 ) . . . . . . . . . B y ( 1 ) a n d ( 2 ) b - 2 a = 2 a s ( a = 0 ) S o , b = 2 T r a n s l a t e y = 2 x b y v e c t o r 0 2 t o g e t y = 2 x + 2

(c) y = 2 x can be transformed to y = 2 x + 2 by a translation of b 0 . Find the value of b .

y = 2 x y = 2 x + 2 ( 1 ) . . . . . . . f ( x - a ) + b = 2 ( x - a ) + b = 2 x - 2 a + b ( 2 ) . . . . . . . . . B y ( 1 ) a n d ( 2 ) b - 2 a = 2 a s ( b = 0 ) S o , a = - 1 Translate y = 2x by vector - 1 0 to get y = 2x +2

The graph of y = x 2 - 4 x + 1 is translated by the vector 1 2 . Find, in the form y = a x 2 + b x + c , the equation of the resulting graph.

Translate y= x 2 -4x+1 by vector 1 2 ⇒ y = ( x - 1 ) 2 - 4 ( x - 1 ) + 1 + 2 ⇒ y = x 2 - 2 x + 1 - 4 x - 4 + 3 ⇒ y = x 2 - 6 x

The graph of y = a x 2 + b x + c is translated by the vector 2 - 5 . The resulting graph is y = 2 x 2 - 11 x + 10 . Find the value of $a$, the value of $b$ and the value of $c$.

Translate y = a x 2 + b x + c by 2 - 5 y = a x - 2 2 + b x - 2 + c - 5 y = a x 2 + 4 - 4 x + b x - 2 + c - 5 y = a x 2 + b - 4 a x + 4 a - 2 b + c - 5 Compare with equation y = 2 x 2 - 11 x + 10 a = 2 b - 4 a = - 11 ⇒ b - 8 = - 11 ⇒ b = - 3 4 a - 2 b + c - 5 = 10 ⇒ 4 2 - 2 - 3 + c = 15 ⇒ c = 1

E M B I B E

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E

Sue Pemberton Solutions for Chapter: Functions, Exercise 6: EXERCISE 2E

Author:Sue Pemberton

Sue Pemberton Mathematics Solutions for Exercise - Sue Pemberton Solutions for Chapter: Functions, Exercise 6: EXERCISE 2E

Attempt the practice questions on Chapter 2: Functions, Exercise 6: EXERCISE 2E with hints and solutions to strengthen your understanding. Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book solutions are prepared by Experienced Embibe Experts.

Questions from Sue Pemberton Solutions for Chapter: Functions, Exercise 6: EXERCISE 2E with Hints & Solutions

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 3

The diagram shows the graph of $y = f (x)$ . Sketch the graphs of each of the following functions.

(b) $y = f (x - 2)$ .

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 3

The diagram shows the graph of $y = f (x)$ . Sketch the graphs of each of the following functions.

(c) $y = f (x + 1) - 5$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 4

(a) On the same diagram, sketch the graphs of $y = 2 x$ and $y = 2 x + 2$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 4

(b) $y = 2 x$ can be transformed to $y = 2 x + 2$ by a translation of $(\begin{array}{l} 0 \\ a \end{array})$ . Find the value of $a$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 4

(c) $y = 2 x$ can be transformed to $y = 2 x + 2$ by a translation of $(\begin{array}{l} b \\ 0 \end{array})$ . Find the value of $b$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 5

A cubic graph has equation $y = (x + 3) (x - 2) (x - 5)$ . Write, in a similar form, the equation of the graph after a translation of $(\begin{array}{l} 2 \\ 0 \end{array})$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 6

The graph of $y = x^{2} - 4 x + 1$ is translated by the vector $(\begin{array}{l} 1 \\ 2 \end{array})$ . Find, in the form $y = a x^{2} + b x + c$ , the equation of the resulting graph.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 1 Course Book>Chapter 2 - Functions>EXERCISE 2E>Q 7

The graph of $y = a x^{2} + b x + c$ is translated by the vector $(\begin{array}{r} 2 \\ - 5 \end{array})$ . The resulting graph is $y = 2 x^{2} - 11 x + 10$ . Find the value of $a$, the value of $b$ and the value of $c$.

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