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GRE Subject Test: Math : Classifying Functions

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Example Questions

Example Question #1 : Classifying Functions

What kind of function is this: $f(x)=\sqrt[3] {x-1}$ ?

Possible Answers:

Cube Function

Rational Function

Square Function

Cube-Root Function

Correct answer:

Cube-Root Function

Explanation:

Step 1: Look at the equation.. $\sqrt[3] {x-1}$ . The cube-root outside of the function determines what the answer is..

The function is a cube-root function.

Note:

Square function, x^2+...
Cube function, x^3+...
Rational function, $\frac {1}{x}$ (if $x\neq 0$ )

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Example Question #11 : Calculus

What kind of function is f(x)=x^3-x^2+3x-1

Possible Answers:

Line

Cubic

Parabola

Hyperbola

Correct answer:

Cubic

Explanation:

Step 1: To classify any function, find the degree of that function. The degree of a function is the highest exponent.

Step 2: Find degree of f(x)=x^3-x^2+3x-1 .

The degree is 3..

Step 3: Find what kind of function has degree of 3:

A cubic function has a degree of 3...

A square function has a degree of 2
A line has a degree of 1

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Example Question #11 : Calculus

What kind of function is $\large y=x^2$

Possible Answers:

Circle

Cubic

Parabola

Line

Correct answer:

Parabola

Explanation:

Step 1: Define some basic graphs and their functions...

Line functions have an equation $\large ax+b$ , where $\large \large \{a,b\}\in \mathbb{R}$
Parabola (Quadratic functions) have an equation $\large ax^2+bx+c$ or $\large ax^2+c$ or $\large ax^2$ , where $\large \large \{a,b,c\}\in \mathbb{R}$

Cubic functions have an equation $\large \large ax^3 \pm b$ , where $\large \{a,b\} \in \mathbb{R}$

Step 2: Determine what type of function is given...

The equation given is a parabola...

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Example Question #3 : Classifying Functions

What kind of function is $\large y=\sqrt[3] {x+6}-4$ ?

Possible Answers:

Reciprocal Function

Cubic Function

Cube-Root Function

Absolute Value

Quadratic Function

Correct answer:

Cube-Root Function

Explanation:

Quadratic functions have at least an $\large x^2$ term.
Absolute Functions have $\large \left | x\right |$ .

Cube-Root functions have $\large \sqrt[3]{x}$

The function $\large y$ is a cube-root function because it shares $\large \sqrt[3]{x}$

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GRE Subject Test: Math : Classifying Functions

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Classifying Functions

Example Question #11 : Calculus

Example Question #11 : Calculus

Example Question #3 : Classifying Functions

All GRE Subject Test: Math Resources

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