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GRE Subject Test: Math : Functions

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

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All GRE Subject Test: Math Resources

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Example Questions

Example Question #11 : Calculus

What is the range of the function?
$f(x) = \begin{cases} x^2, & x>2\\ -x+1, & x\leq 2 \end{cases} \bigg\}$

Possible Answers:

(-2,2)

$(-\infty,-1]\cup [9,+\infty)$

$[0,+\infty)$

$(-\infty, +\infty)$

Correct answer:

$(-\infty,-1]\cup [9,+\infty)$

Explanation:

Step 1: Find the minimum and maximum range for each equation..

Let's start with x^2, x>2 ..

I will plug in , I get . This is in my domain, which means it's the lowest value for the range. The maximum value is $+\infty$

$-x+1, x\leq 2$

Minimum range: $-\infty$

Maximum range:

Step 2: Write the solution in interval notation form:

$-\infty, +\infty$ always get parentheses

9, -1 get brackets because they are in my range...

Answer:

$(-\infty, -1] \cup [9,+\infty)$

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Example Question #1 : Graphing Functions

At what point does the line 2x-y=4 cross the y-axis?

Possible Answers:

(2,0)

(1,2)

(0,-4)

(0,4)

Correct answer:

(0,-4)

Explanation:

Step 1: Rearrange the terms into the form y=mx+b. Move the to the other side.

2x=y+4

Step 2: Move the 4 to the other side.

y=2x-4

Step 3: When the line crosses the y-axis, the x value is zero. We will plug in for x and find the y value.

y=2(0)-4
$\rightarrow y=-4$

So, the point where this line crosses the y-axis is (0,-4)

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Example Question #1 : Classifying Functions

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

Possible Answers:

Cube Function

Cube-Root Function

Square Function

Rational 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 #12 : Functions And Graphs

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

Possible Answers:

Line

Hyperbola

Cubic

Parabola

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 #3 : Classifying Functions

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

Possible Answers:

Parabola

Cubic

Line

Circle

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 #2 : Classifying Functions

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

Possible Answers:

Quadratic Function

Absolute Value

Cubic Function

Cube-Root Function

Reciprocal 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 : Functions

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Calculus

Example Question #1 : Graphing Functions

Example Question #1 : Classifying Functions

Example Question #12 : Functions And Graphs

Example Question #3 : Classifying Functions

Example Question #2 : Classifying Functions

All GRE Subject Test: Math Resources

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