Classifying Functions

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GRE Quantitative Reasoning › Classifying Functions

Questions 1 - 4

1

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

Cube-Root Function

Square Function

Cube Function

Rational 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,
Cube function,
Rational function, $\frac {1}{x}$ (if )

2

What kind of function is

Cubic

Parabola

Line

Hyperbola

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 .

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

3

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

Parabola

Line

Circle

Cubic

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...

4

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

Cube-Root Function

Cubic Function

Quadratic Function

Absolute Value

Reciprocal 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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