Functions

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GRE Quantitative Reasoning › Functions

Questions 1 - 10
1

At what point does the line cross the y-axis?

Explanation

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

Step 2: Move the 4 to the other side.

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.


So, the point where this line crosses the y-axis is

2

What kind of function is this: ?

Cube-Root Function

Square Function

Cube Function

Rational Function

Explanation

Step 1: Look at the equation.. . 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, (if )

3

At what point does the line cross the y-axis?

Explanation

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

Step 2: Move the 4 to the other side.

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.


So, the point where this line crosses the y-axis is

4

What kind of function is this: ?

Cube-Root Function

Square Function

Cube Function

Rational Function

Explanation

Step 1: Look at the equation.. . 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, (if )

5

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

6

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

7

What is the domain of the function ?

the domain is all

the domain is all

the domain is all

the domain is all

Explanation

For a function defined by an expression with variable the domain of is the set of all real numbers that the variable can take such that the expression defining the function is real.

The expression defining function contains a square root.

.

The domain is the set of all first elements of ordered pairs or

Because there cannot be a negative inside the radical sign, set the inside of the radical and solve. The expression under the radical has to satisfy the condition for the function to take real values.

Solve:

Subtract from both sides of the equation.

Divide both sides of the equation by .

Because you are dividing both sides of the equation by a negative integer this will change the sign from to .

The domain or d is all

8

What is the domain of the function ?

the domain is all

the domain is all

the domain is all

the domain is all

Explanation

For a function defined by an expression with variable the domain of is the set of all real numbers that the variable can take such that the expression defining the function is real.

The expression defining function contains a square root.

.

The domain is the set of all first elements of ordered pairs or

Because there cannot be a negative inside the radical sign, set the inside of the radical and solve. The expression under the radical has to satisfy the condition for the function to take real values.

Solve:

Subtract from both sides of the equation.

Divide both sides of the equation by .

Because you are dividing both sides of the equation by a negative integer this will change the sign from to .

The domain or d is all

9

What is the domain and the range for this set of numbers?

domain is and the range is

domain is and the range is

domain is and the range is

domain is and the range is

Explanation

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).

Given this set of ordered pairs , the

domain is and the range is .

Note: If a value of a coordinate is repeated, it only gets listed once in the set.

10

What is the domain and the range for this set of numbers?

domain is and the range is

domain is and the range is

domain is and the range is

domain is and the range is

Explanation

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates).

Given this set of ordered pairs , the

domain is and the range is .

Note: If a value of a coordinate is repeated, it only gets listed once in the set.

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