3.2, 3.3, 3.6 Review Flashcard

Front

What are excluded values in a rational function?

Back

Excluded values are the values of the variable that make the denominator of a rational function equal to zero, as these values are not in the domain of the function.

Front

How do you find the excluded values of the function \( \frac{x(x+4)}{x^2-16} \)?

Back

Set the denominator equal to zero: \( x^2 - 16 = 0 \). This factors to \( (x-4)(x+4) = 0 \), giving excluded values of \( x = -4 \) and \( x = 4 \).

Front

What is an x-intercept of a function?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, which occurs when the output (y-value) is zero.

Front

How do you find the x-intercept of a rational function?

Back

To find the x-intercept, set the numerator equal to zero and solve for the variable.

Front

What is the x-intercept of the rational function given in the quiz?

Back

The x-intercept is \( \left( \frac{5}{2}, 0 \right) \).

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable that make the equation true.

Front

What is the solution to the equation provided in the quiz?

Back

The solution is \( x = -3 \).

Front

How do you simplify the expression \( \frac{15x^2}{5x^3} \)?

Back

Divide the coefficients and subtract the exponents of like bases: \( \frac{15}{5} = 3 \) and \( x^{2-3} = x^{-1} = \frac{3}{x} \).

Front

What is the simplified form of \( \frac{15x^2}{5x^3} \)?

Back

The simplified form is \( \frac{3}{x} \).

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.