What is the inverse of the function $$f(x)=\frac{1}{3}(x+3)^2-5;\ x\le-3$$ ?

The inverse is $$f^{-1}(x)=-\sqrt{3x+15}-3$$ .

What is the equation of the function g obtained from f using composite transformation if g is represented as $$g(x)=\sqrt[3]{x+2}-4$$ ?

The equation is $$g(x)=\sqrt[3]{x+2}-4$$ .

Solve the equation $$\left(x-3\right)^{\frac{2}{5}}=4$$ .

The solutions are $$x=35\ or\ x=-29$$ .

What is the domain of the function $$f(x)=\sqrt{x}$$ ?

The domain is all non-negative real numbers, i.e., $$[0, \infty)$$ .

What is the range of the function $$f(x)=\sqrt{x}$$ ?

The range is all non-negative real numbers, i.e., $$[0, \infty)$$ .

What is the effect of a vertical shift on the graph of a function?

A vertical shift moves the graph up or down without changing its shape.

What does the notation $$f^{-1}(x)$$ represent?

It represents the inverse function of f(x).

How do you find the inverse of a function algebraically?

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

What is the significance of the horizontal line test?

If a horizontal line intersects the graph of a function more than once, the function does not have an inverse.

What is a composite function?

A composite function is formed when one function is applied to the result of another function, denoted as $$(f \circ g)(x) = f(g(x))$$ .

What is the general form of a cubic root function?

The general form is $$f(x)=\sqrt[3]{x}$$ .

What is the transformation of the function $$f(x)=\sqrt[3]{x}$$ to obtain $$g(x)=\sqrt[3]{x+2}-4$$ ?

The transformation involves a horizontal shift left by 2 units and a vertical shift down by 4 units.

Radical Functions Test Review

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-BF.B.4A, HSF.BF.B.3, HSA.REI.A.2

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15 questions

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FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.B.3

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

How do you determine if two functions f(x) and g(x) are inverses using composition?

Back

Tags

CCSS.HSF-BF.B.4B

FLASHCARD QUESTION

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (root) symbol.

FLASHCARD QUESTION

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Back

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