Y2,C2 - Functions & Graphs

Question 1

What is a function

Answer 1

When every element of the domain is mapped to exactly ONE element of the range
(one to one)

Question 2

Is a many-to-one relationship a function

Answer 2

Yes, each input maps to ONE output

Question 3

Is a one-to-many relationship a function

Answer 3

No, each input maps to more than ONE output

Question 4

Is a one-to-one relationship a function

Answer 4

Yes, each input maps to ONE output

Question 5

f(x) = x^2 + 1
g(x) = 4x - 2
What is fg(x)

Answer 5

(4x-2)^2 +1

Question 6

f(x) = x^2 + 1
g(x) = 4x - 2
What is gf(x)

Answer 6

4(x^2 + 1) - 2

Question 7

Why must a function be one-to-one to have an inverse

Answer 7

Many-to-one inverse would be one-to-many which is NOT a function

Question 8

How does the domain and range of f(x) and f^-1(x) relate

Answer 8

The domain of f(x) is the range of f^-1(x)
The range of f(x) is the domain of f^-1(x)

Question 9

What is the line of reflection of a function and it’s inverse

Answer 9

y = x

Question 10

What is the range of e^2 + 2

Answer 10

Range of e^x:
f(x) > 0
Therefore range of e^2 + 2:
f(x) > 2

Question 11

How to draw l f(x) l

Answer 11

Reflect negative y values to positive

Question 12

How to draw f(l x l)

Answer 12

Reflect positive x values to negative across y axis
(reflection of y = f(x) for x>= 0 in the y axis)

Question 13

What transformation is f(x+2)

Answer 13

Shift 2 to the left

Question 14

What transformation is 2f(x)

Answer 14

Double y coordinates

Question 15

What transformation is f(2x)

Answer 15

Half x coordinates

Question 16

What transformation is -f(x)

Answer 16

Negate y coordinates

Question 17

Transformation of l f(-x) l

Answer 17

Negate x coordinates
Reflect negative y values to positive

Question 18

Find f^-1(x) when f(x) = x^2 + 6x - 4

Answer 18

Complete square: y = (x + 3)^2 - 13
y + 13 = (x + 3)^2
sqr(y + 13) = x + 3
sqr(y + 13) - 3 = x
Therefore f^-1(x) = sqr(x + 13) - 3