Question 1

Which of the following best describes a rational function?

Accepted Answer

A function that is expressed as a ratio of two polynomials.

Answer

A function that only uses linear equations.

Answer

A function that contains an infinite number of terms.

Answer

A function that includes only multiplication and division.

Question 2

Which of the following represents a rational equation?

Accepted Answer

7x/(x-3) = 5

Answer

x^2 + 1 = 0

Answer

2x + 1 < 5

Answer

3x > 8

Question 3

What distinguishes a rational inequality from a rational equation?

Accepted Answer

It involves an inequality symbol rather than an equal sign.

Answer

It can only contain integers.

Answer

It must involve addition and subtraction only.

Answer

It has no variables present.

Question 4

What is the first step in solving the rational equation 4/(x+2) = 3?

Accepted Answer

Multiply both sides by (x+2).

Answer

Add 2 to both sides.

Answer

Subtract 4 from both sides.

Answer

Change the equation to an inequality.

Question 5

When solving the inequality (x-1)/(x+3) > 0, what should be considered about the values that make the denominator zero?

Accepted Answer

These values are not included in the solution because they make the expression undefined.

Answer

These values indicate where the expression equals zero.

Answer

These values help find the solutions to the inequality.

Answer

These values do not affect the solution.

Question 6

In solving the inequality (2-x)/(x+5) > 0, what do the critical values from the numerator and denominator help determine?

Accepted Answer

They divide the number line into intervals for testing.

Answer

They simplify the expressions involved.

Answer

They indicate where the inequality is equal to one.

Answer

They identify the exact solutions of the inequality.

Question 7

Why do we exclude x=-5 from the solutions of the equation 2/(x+5) = 4?

Accepted Answer

Because x=-5 results in an undefined expression.

Answer

Because x=-5 results in a zero in the numerator.

Answer

Because x=-5 leads to an extraneous solution.

Answer

Because x=-5 changes the inequality direction.

Question 8

In the inequality (x-3)/(x+1) > 0, what does it indicate if x=-1 makes the denominator zero?

Accepted Answer

x=-1 must be excluded from the solution.

Answer

x=-1 is the only solution.

Answer

x=-1 makes the inequality false.

Answer

x=-1 is a solution to the inequality.

Question 9

What is the solution to 6x = 18?

Accepted Answer

x = 3

Answer

x = 1.5

Answer

x = 4

Answer

x = 9/2

Question 10

What is the value of x in the equation (5x+2)/(-x-4) = 1?

Accepted Answer

x = -1

Answer

x = 2

Answer

x = 10

Answer

x = 4

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