Evaluate $$f(g(x))$$ if $$f(x)=x+2$$ and $$g(x)=x^2-4$$ .

$$f(g(x)) = f(x^2 - 4) = (x^2 - 4) + 2 = x^2 - 2$$ .

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

The domain of $$f(x) = \sqrt{x}$$ is $$[0, \infty)$$ .

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

The range of $$f(x) = \sqrt{x}$$ is $$[0, \infty)$$ .

What is the effect of a negative sign in front of a radical function?

A negative sign reflects the graph of the function across the x-axis.

What is the vertical line test?

The vertical line test is a method to determine if a curve is a function by checking if any vertical line intersects the curve at more than one point.

What is the definition of a composite function?

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

What is the formula for the sum of two functions?

The sum of two functions $$f(x)$$ and $$g(x)$$ is given by $$(f + g)(x) = f(x) + g(x)$$ .

What is the definition of an inverse function?

An inverse function reverses the operation of the original function, such that if $$f(a) = b$$ , then $$f^{-1}(b) = a$$ .

What is the significance of the discriminant in quadratic functions?

The discriminant determines the nature of the roots of a quadratic equation: if positive, two real roots; if zero, one real root; if negative, no real roots.

How do you simplify a radical expression?

To simplify a radical expression, factor out perfect squares (or cubes) from under the radical.

What is the relationship between a function and its inverse?

A function and its inverse are reflections of each other across the line $$y = x$$ .

Unit 4 Radical Functions Flashcard 1 Review

Flashcard

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-BF.A.1C, HSF-BF.B.4A, HSF-IF.C.7B

Standards-aligned

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FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.A.1C

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

Tags

CCSS.HSF-BF.A.1C

FLASHCARD QUESTION

Front

What is the definition of a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.).

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

How do you find the inverse of a function algebraically?

Back

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

Tags

CCSS.HSF-BF.B.4A

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