Graphing Logarithmic Functions

Tim Brzezinski, Mar 22, 2024

Graphing Logarithmic Functions

Table of Contents

  1. Exploration
    1. What if the Exponent is an OUTPUT?
    2. Part 1
    3. Part 2
    4. Part 3
  2. You Try!
    1. You Try It! Graphing Logarithmic Functions
    2. You Try it: Writing Logarithmic Functions

1.

Exploration

  • 1. What if the Exponent is an OUTPUT?
  • 2. Part 1
  • 3. Part 2
  • 4. Part 3

1.1.

What if the Exponent is an OUTPUT?

(1) Move the LARGE POINT on the xAxis anywhere you want. (2) Press ANIMATE. (3) Press RECORD TRACE. Repeat steps (1)-(3) in that order for many times.
Recall the graph of [math]y=2^x[/math] has a horizontal asymptote at [math]y=0[/math] because it was impossible to raise 2 to any exponent and get a negative output. [br][br]Does the graph of [math]x=2^y[/math] or [math]y=\log_2\left(x\right)[/math] have any asymptote? If so, what kind? and what would its equation be?
What is the domain (set of all allowable inputs) of the function [math]y=\log_2\left(x\right)[/math]?
What is the range (set of all outputs) of the function [math]y=\log_2\left(x\right)[/math]?
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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2.

You Try!

  • 1. You Try It! Graphing Logarithmic Functions
  • 2. You Try it: Writing Logarithmic Functions

2.1.

You Try It! Graphing Logarithmic Functions

Move the LARGE POINT(S) and/or slider below to construct the graph of the logarithmic function shown.
Move the LARGE POINT(S) and/or slider below to construct the graph of the logarithmic function shown.
Move the LARGE POINT(S) and/or slider below to construct the graph of the logarithmic function shown.
Move the LARGE POINT(S) and/or slider below to construct the graph of the logarithmic function shown.
– Tim Brzezinski

2.2.

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