Graphs & Functions

Question 1

Movement of Graphs
f(x)+2

Answer 1

the y co-ord (x,y)

+2 moves up

-2 moves down

Question 2

Movement of Graphs
f(x-2)

Answer 2

to the x co-ord (x,y)

-2 moves to the right
+2 moves to the left

Question 3

Movement of Graphs
y = 4f(x)

Answer 3

to the y co-ord (vertical)

k is bigger than 1 stretches (xk)
k is less than 1 compress (xk)

Question 4

Movement of Graphs
y = f(2x)

Answer 4

to the x co-ord (horizontally)

k is bigger than 1 compress (x divided by k)

k is less than 1 stretch (x divided by k)

Question 5

Domain
if it is in the form of a fraction

Answer 5

x+4 doesn’t not equal 0
x does not equal -4
xER : x does not equal -4

Question 6

Domain
if it is in the form of a square root

Answer 6

x-3 > 0
x > 3
xER : x > 3

Question 7

Composite Function

f(x) = x+1 g(x) = x^2 + 2x + 1

Answer 7

f(g(x))
f(g(x)) = (x^2 + 2x +1) + 1
= x^2 + 2x + 2

Question 8

Inverse Function

Answer 8

f(x) = x^2 - 3
y = x^2 -3

swap the y and the x
x = y^2 -3

rearrange to y =
y ^2 = x + 3
y = square root x+3

change y into f^-1(x)

Question 9

Expontential graphs

Find the value of a (3,8)

Answer 9

sub co-ords into y = a^x
8= a^3
a = 3 square root of 8
y = 2^x

Question 10

Expontential graphs

Find a and b

2 (3,9)

Answer 10

from 1 it increased by 1 to get to 2
b = 1

9= a^3 = 1
a^3 = 8
a = 2