Logarithmic Functions and Their Properties

Logarithmic Functions and Their Properties

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to find the domain and vertical asymptotes of logarithmic functions. It covers basic logarithmic functions, their domains, and vertical asymptotes at x=0. The tutorial then explores how shifting the function affects these properties. It provides examples of linear and quadratic logarithmic functions, demonstrating how to determine their domains and vertical asymptotes using algebraic methods.

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25 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the domain of a basic logarithmic function y = log(x)?

x > 0

x < 0

x ≥ 0

x ≤ 0

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Where is the vertical asymptote located for the function y = log(x)?

y = 1

x = 1

y = 0

x = 0

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does shifting a logarithmic function to the left affect its vertical asymptote?

It moves the asymptote downwards.

It moves the asymptote upwards.

It moves the asymptote to the right.

It moves the asymptote to the left.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the graph of y = log(x) when it is shifted two units to the left?

The vertical asymptote moves to x = -2.

The vertical asymptote moves to y = 2.

The vertical asymptote moves to x = 2.

The vertical asymptote remains at x = 0.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the function y = log(x + 2), what is the vertical asymptote?

x = 1

x = 0

x = -2

x = 2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

x ≥ -2

x < -2

x > -2

x = -2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the effect of shifting the function y = log(x) to the right by 2 units?

The vertical asymptote moves to x = 2.

The vertical asymptote moves to x = -2.

The vertical asymptote moves to y = 2.

The vertical asymptote remains at x = 0.

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