Graphing Exponential and Logarithmic Functions Through Transformations

What is the first step in finding the inverse of a logarithmic or exponential function?

• Isolate the variable Y

• Convert the function into an exponential form

• None of the above

• Rewrite and swap X and Y variables

What is the result of swapping X and Y in the function notation?

• It has no effect on the function

• It prepares the function for inversion

• It helps in isolating the variable Y

• It simplifies the function

What must be done after rewriting the function with swapped variables?

• Add one to both sides

• Isolate the logarithmic expression

• Divide both sides by two

• Multiply both sides by two

What does isolating the logarithmic expression involve?

• Getting the logarithmic part by itself

• Applying logarithmic rules

• Combining all terms on one side

• None of the above

What transformation is applied to the function to invert the inputs and outputs?

• Subtraction of constants

• Conversion from logarithmic to exponential

• Addition of constants

• None of the above

What is the purpose of inverting inputs and outputs in the function?

• To transform the function type

• To prepare for solving Y

• To correct an error in the initial function

• To simplify the calculation

What is achieved by converting the logarithmic function to an exponential function?

• It reverses the function's behavior

• It has no significant impact

• It complicates the function further

• It allows for easier manipulation

How do you solve for Y in the final steps?

• None of the above

• Add one to both sides and multiply by one half

• Subtract one from both sides

• Multiply both sides by two

What mathematical operation is used in the final step to solve for Y?

• Multiplication

• Addition

• Division

• Subtraction

How is the function notation rewritten at the end?

• As a simple exponential function

• As a complex logarithmic function

• None of the above

• As a simplified version of the original function