Exponential Functions Unit Part 4

Question 1

What brackets do you use for domain and range if the domain/range is between two values?

Answer 1

()

because if you use {} that means that the two values given are the only numbers in the domain and range

Question 2

What happens to the domain and range when you graph logarithmic functions?

Answer 2

They switch

example:
domain = (negative infinity, infinity) and range = (-1, infinity)
→
domain = (-1, infinity) and range = (negative infinity, infinity)

Question 3

What happens to a horizontal asymptote when you graph logarithmic functions?

Answer 3

The variable switches

example:
y = -1
→
x = -1

Question 4

What is the product property of logs?

Answer 4

log_b^mn = log_b^m + log_b^n (when an argument is being multiplied to a number you can create two logarithmic functions and add them together to represent this)

Question 5

What is the quotient property of logs?

Answer 5

log_b^m/n = log_b^m - log_b^n (when an argument is being divided by a number you can create two logarithmic functions and subtract them to represent this)

Question 6

What is the exponent property of logs?

Answer 6

log_b^m^n = nlog_b^m (when the argument is being raised to a number you can bring that number up to the front of the function)

Question 7

What is the change of base rule?

Answer 7

log_b^m = log_c^m/log_c^b (the base of c cancels out (c = real number))

Question 8

What is a common log?

Answer 8

log 100 = log_10^100 (base is always 10)

Question 9

What is a natural log?

Answer 9

ln 1 = log_e^1 (e = 2.178…)