1: Functions

Question 1

Define domain

Answer 1

(x-values) Set of all the 1st numbers of the ordered pairs

Question 2

Define range

Answer 2

(y-values) Set of all the 2nd numbers of the ordered pairs

Question 3

What is the domain and range?

{(1,4),(2,7),(3,10),(4,13)}

Answer 3

Domain: {1,2,3,4}

Range: {4,7,10,13}

Question 4

What are the big ALWAYS and NO when it comes to domain and range?

Answer 4

Do NOT repeat the value twice and ALWAYS write in order

Question 5

Define function

Answer 5

Math relation. Domain is associated with ONE element of the range. If no ordered pairs have the same 1st element, then it is not a function but a relation.

Question 6

What does {,} mean?

Answer 6

“The set of”

Question 7

What can you found by the vertical line test?

Answer 7

That a relation is a function IF any vertical line drawn will not intersect more than once

Question 8

Define asymptote

Answer 8

Imagine an invisible line that a graph approaches, but do not intersect.

Infinity; it gets closer, but never reaches for e.g. y = 0 or x = 0

Question 9

What is a composite function?

Answer 9

• It’s a combination function
• f(g(x)) = (f o g)(x)
• Put in function f in function g.

Question 10

What is an inverse function?

Answer 10

• It reverses the action of that function
• Inverse of f(x) is written f^-1(x)

Question 11

What can you find out by the horizontal line test?

Answer 11

• Identify inverse functions.
• If a horizontal line crosses the graph of a function more than once = NOT an inverse function!

Question 12

How can you find the inverse of a function?

Answer 12

• The function is a reflection from the line y=x
• y=x is a straight line from origo

Question 13

How can you find the inverse of a function algebraically?

Answer 13

1. Replace f(x) with y
2. Replace all y with x and all x with y
3. Make y the subject
4. Replace y with f^-1(x)

Question 14

What is an identity function?

Answer 14

• Function I (x) = x
• Leaves x unchanged
• f o f^-1 = I

Question 15

What are the four directions you can TRANSLATE a function?

Answer 15

• Up
• Down
• Left
• Right

Question 16

What are the two “directions” you can REFLECT a function?

Answer 16

• The x-axis
• The y-axis

Question 17

What are the two “directions” you can STRETCH a function?

Answer 17

• Horizontal
• Vertical

Question 18

What are the four f(x) functions for translating a function?

Answer 18

• Up = f(x) + k
• Down = f(x) - k
• Left = f(x + k)
• Right = f(x - k)

Question 19

What are the two f(x) functions for reflection?

Answer 19

• x-axis = -f(x)
• y-axis = f(-x)

Question 20

What are the two f(x) functions for stretches?

Answer 20

• f(qx) stretches or compresses f(x) horizontally with scale factor 1/q
  
  • When q > 1 = compressed towards the y-axis
  • When 0 < q < 1 = stretched away from the y-axis
• pf(x) stretches f(x) vertically with scale factor p
  
  • When 0 < p < 1 = graph is compressed towards the x-axis
  • When p > 1 = stretches away from x-axis