Understanding Rational Functions Concepts

The video tutorial covers graphing rational functions, finding intercepts, and identifying asymptotes and holes. It explains how to solve rational equations and check for extraneous solutions. The teacher uses examples to illustrate concepts like horizontal and vertical shifts, common factors, and domain restrictions.

What is the y-intercept of a rational function if you plug in 0 for x and get -14/5?

• (0, -14/5)

• (0, 14/5)

• (0, -5/14)

• (0, 5/14)

If a rational function has a common factor in the numerator and denominator, what should you do first?

• Add them together

• Subtract them

• Factor them out

• Ignore them

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

• Set y to 0 and solve for x

• Find the asymptotes

• Set x to 0 and solve for y

• Find the slope

What is a 'hole' in a rational function?

• A point where the graph has a vertical asymptote

• A point where the graph crosses the x-axis

• A point where the graph crosses the y-axis

• A point where the function is undefined due to a canceled factor

What is the domain of a rational function?

• All negative numbers

• All positive numbers

• All real numbers except where the denominator is zero

• All real numbers

How do you determine a vertical asymptote in a rational function?

• Set the numerator to zero

• Find the y-intercept

• Set the denominator to zero

• Find the slope

What is the result of synthetic division used for in rational functions?

• Finding the vertical asymptote

• Finding the slant asymptote

• Finding the x-intercept

• Finding the y-intercept

When solving rational equations, what must you check for in your solutions?

• If they are negative

• If they are positive

• If they are integers

• If they make the denominator zero

What is an extraneous solution in the context of rational equations?

• A solution that makes the numerator zero

• A solution that does not satisfy the equation

• A solution that makes the denominator zero

• A solution that satisfies the equation

How do you solve a rational equation with different denominators?

• Find a common denominator

• Multiply the numerators

• Subtract the numerators

• Add the numerators