Q3. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

 

If the line $x=a$ is a vertical asymptote of a rational function, then a is an excluded value.

Step-by-Step Solution

Answer

The given statement is true.

Step 1. State the concept of excluded value of a rational function.

A rational function is an algebraic expression whose numerator and denominator are polynomials. Also, division by 0 is undefined, so therefore, the polynomials in the denominator cannot be zero and the values for which the denominator is zero is termed as excluded values for the respective rational expression.

Step 2. Explanation of the statement.

It is given that the equation of line $x=a$ is a vertical asymptote for the rational function. 

So, $x=a$ is a vertical asymptote for the rational function. 

Hence, value of a is known as excluded value.

Step 3. Write whether the statement is true or false.

The given statement “If the line $x=a$ is a vertical asymptote of a rational function, then a is an excluded value.” is true.