What is the inverse function of $$f(x) = 2x^3 - 3$$ ?

The inverse function is $$f^{-1}(x) = \frac{\text{cube root}(x + 3)}{2}$$ .

For which domain restrictions of x will $$f(x) = 2(x - 3)^2 + 5$$ be invertible?

The function is invertible for $$x \ge 3$$ .

What is the radical function represented by the transformation of the parent function $$f(x) = \sqrt{x}$$ ?

The function is $$f(x) = \sqrt{x - 2} + 5$$ .

How do you determine if a function is invertible using its graph?

A function is invertible if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once.

What is the general form of an inverse function?

The general form of an inverse function is $$f^{-1}(x)$$ , which undoes the action of the original function $$f(x)$$ .

What is the relationship between a function and its inverse?

The relationship is that if $$f(a) = b$$ , then $$f^{-1}(b) = a$$ .

What is the process to find the inverse of a function algebraically?

To find the inverse, swap the x and y in the equation and solve for y.

What is a parent function?

A parent function is the simplest form of a function type, from which other functions can be derived by transformations.

What transformations can be applied to the parent function $$f(x) = \sqrt{x}$$ ?

Transformations include translations, reflections, stretches, and compressions.

What does it mean for a function to be non-invertible?

A non-invertible function does not have a unique inverse, often because it fails the horizontal line test.

How can you verify if a function is invertible using its derivative?

If the derivative of the function is always positive or always negative, the function is one-to-one and thus invertible.

Adv Algebra M3.T1 Formative 1 Practice Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

2.

FLASHCARD QUESTION

Front

Back

Yes, it is invertible.

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4D

4.

FLASHCARD QUESTION

Front

Back

Yes, it is invertible.

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.3

6.

FLASHCARD QUESTION

Front

Define an invertible function.

Back

An invertible function is a function that has an inverse, meaning for every output there is a unique input.

Tags

CCSS.HSF-BF.B.4D

7.

FLASHCARD QUESTION

Front

What is the significance of a function being one-to-one?

Back

A one-to-one function is significant because it ensures that each output corresponds to exactly one input, which is necessary for the function to be invertible.

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