FINDING DOMAIN RANGE INTERCEPTS OF LOGARITHMIC FUNCTION WORKSHEET

For the following exercises, state the domain, range, and x- and y-intercepts, if they exist. If they do not exist, write DNE.

Problem 1 :

h(x) = log₄(x - 1) + 1

Problem 2 :

f(x) = log(5x + 10) + 3

Problem 3 :

g(x) = ln(-x) - 2

Problem 4 :

f(x) = log₂(x + 2) - 5

Problem 5 :

h(x) = 3ln(x) - 9

Answer Key

1) Domain is x > 1

All real numbers.

x- intercept is (5/4, 0)

y-intercept is does not exist

2) Domain: {x € R |x > -2}

Range is set of real numbers.

x-intercept is x = -9999/5000

y-intercept is y = 4

3) Domain: (-∞, 0)

All real numbers

x = -e²

Does not exist.

4) Domain: (-2, ∞)

All real numbers

x = 30

f(0) = -4

5) Domain: (0, ∞)

All real numbers

x = e³

Does not exist.