Exponential and Logarithmic Functions

Question 1

Exponent: f(x) = Aˣ (parent function)

Answer 1

• g(x) = af(bx - c) + d
• = a(Aᵇˣ ⁻ ᶜ) + d

Question 2

Asymptote of g(x)

Answer 2

• HA: y = d
• R: y ∈ (d, ∞)

Question 3

Logarithm: f⁻¹(x)

Answer 3

= log(A) x

Question 4

Asymptote of log x

Answer 4

• VA: x = d
• D: x ∈ (d, ∞)

Question 5

log(c) a = b

Answer 5

a = cᵇ

Question 5

Invariant Points for all bases (excluding transitions and reflections)

Answer 5

• Exponent: (0, 1)
• Logarithm: (1, 0)

Question 6

log AB

Answer 6

= log A + log B

Question 7

Intersection Points for function and inverse

Answer 7

f(x) = x

Question 8

log(b) Aⁿ

Answer 8

• = n log(b) A, b ∈ R
• ≠ log(b) (A)ⁿ

Question 9

log A/B

Answer 9

= log A - log B

Question 10

log(b) A

Answer 10

= log(c) A/log(c) b

Question 10

Aⁿ

Answer 10

• = 10ⁿ ˡᵒᵍ ᴬ
• = 10⁽ˡᵒᵍ ᴬ⁾ ⁿ