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Logs domain and range

Total questions: 15

Worksheet time: 3hrs 30mins

Name
Class
Date
1.

Describe domain of the function shown: y=log2(x+1)

2.

Describe range of the function shown: y=log2(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

3.

Find the asymptote of the following:  y = -6 + log10 x

4.
What kind of asymptotes do logs have?
a)
horizontal ( y=0)
b)
vertical (x=0)
5.
find the asymptote: y = log10 (x+3)
6.

Identify the asymptote for the function ℎ(𝑥) = 𝑙𝑛(𝑥 − 1) + 3.

7.

Which graph correctly shows the asymptote of f(x)=log⁡(x+2)+3f(x)=\log(x+2)+3  

a)
b)
c)
d)
8.

Match the following graphs with their domains

a)
1.

Domian: x > -2

b)
2.

Domian: x > 3

c)
3.

Domian: x > 0

d)
4.

Domian: x > 2

9.

What is the domain?

(inequality notation)

10.

f(x)=log5(x+4) - 2

Describe the asymptote

11.

f(x)=log5(x+4) - 2

Find the Domain and Range

a)

Domain: x ≥ -4

Range: all real numbers

b)

Domain: all real numbers

Range: y ≥ -4

c)

Domain: all real numbers

Range: y > -4

d)

Domain: x > -4

Range: all real numbers

12.

The domain of

log⁡(2x+8)−3\log\left(2x+8\right)-3

in inequality notation

13.

The domain of

log⁡(x−10)−3\log\left(x-10\right)-3

in inequality notation

14.

sketch

y = log (x-2)

15.

sketch

y = -log(x-5)