Additional Functions

Question 1

Invariable Coordinate

Answer 1

A coordinate that doesn’t change from the transformation of a function.

Question 2

Reflections

Answer 2

• X - Axis: y = - f(x)
• Y - Axis: y = f(-x)

Question 3

Vertical multiplication by a factor of |a|, |a|> 1

Answer 3

• y = af(x)
• Invariable Coordinates: y=0

Question 4

• Vertical translation up, k > 0
• Horizontal translation right, h > 0

Answer 4

y = f(x - h) + k

Question 5

Horizontal DIVIDE by a factor of |k|, |k|> 1

Answer 5

• f(kx)
• Invariable Coordinates: x = 0

Question 6

Reciprocal Function Domain/Range

Answer 6

D: {x ∈ R | x ≠ n}
R: {y ∈ R | y ≠ k}

Question 7

Square Root Function Domain/Range

Answer 7

D: x ∈ [m, ထ)
R: y ∈ [k, ထ)

Question 8

Semicircle Function Domain/Range

Answer 8

D: x ∈ [-r, r]
R: y ∈ [0, r]

Question 9

Composite Function Symbol

Answer 9

f*g(x) = f(g(x))

Question 10

Properties of Inverse Functions

Answer 10

• f^-1f(x) = ff^-1(x) = x
• f(x) = f^-1(y), f(y) = f^-1(x)

Question 11

Self Inverse Functions

Answer 11

f(x) = f^-1(x)

Question 12

Odd Function Properties

Answer 12

• f(-x) = -f(x)
• h = 0, k = 0

Question 13

Odd Function X Exponents

Answer 13

All x exponents are odd

Question 14

Even Function Properties

Answer 14

• f(-x) = f(x)
• h=0

Question 15

Even Function X Exponents

Answer 15

All x exponents are even (including x^0)