Logarithmic Functions: Domain and Range

This video tutorial explains how to find the domain and range of various logarithmic functions. It provides detailed examples, starting with simple functions and progressing to more complex ones. Each example involves determining the domain by setting the argument of the logarithm greater than zero and finding the range, which is always all real numbers for logarithmic functions. The video concludes with a summary of the key points covered.

What is the domain of the function y = log(x) base 2?

• x ≥ 0

• x < 0

• x ≤ 0

• x > 0

What is the range of the function y = log(x) base 2?

• All real numbers

• y < 0

• y ≥ 0

• y > 0

For the function y = log(x + 2) base 2 - 3, what is the domain?

• x ≤ -2

• x ≥ -2

• x < -2

• x > -2

What is the range of the function y = log(x + 2) base 2 - 3?

• y > -3

• y < -3

• y ≥ -3

• All real numbers

For the function y = log(2x - 1) base 3 - 4, what is the domain?

• x > 1/2

• x < 1/2

• x ≤ 1/2

• x ≥ 1/2

What is the range of the function y = log(2x - 1) base 3 - 4?

• All real numbers

• y < -4

• y > -4

• y ≥ -4

For the function y = log(5 - 2x) - 1, what is the domain?

• x > 5/2

• x < 5/2

• x ≥ 5/2

• x ≤ 5/2

What is the range of the function y = log(5 - 2x) - 1?

• All real numbers

• y < -1

• y > -1

• y ≥ -1

For the function y = log(4x + 8) base 1/2 + 1, what is the domain?

• x ≤ -2

• x ≥ -2

• x < -2

• x > -2

What is the range of the function y = log(4x + 8) base 1/2 + 1?

• y ≥ 1

• All real numbers

• y < 1

• y > 1