M3 Rational Functions Review + Old Stuff

Front

What is a rational function?

Back

Front

How do you divide rational expressions?

Back

Front

What is the process to find the horizontal asymptote of a rational function?

Back

Front

What does the notation |x| mean in inequalities?

Back

The notation |x| represents the absolute value of x, which is the distance of x from 0 on the number line, always non-negative.

Front

How do you solve the inequality |p + 3| ≥ 10?

Back

To solve |p + 3| ≥ 10, split into two cases: p + 3 ≥ 10 and p + 3 ≤ -10, leading to p ≥ 7 or p ≤ -13.

Front

What is the solution to the equation 2^x = 4^(x+1)?

Back

Rewrite 4 as 2^2: 2^x = (2^2)^(x+1) = 2^(2x + 2). Set exponents equal: x = 2x + 2, leading to x = -2.

Front

What is the formula for finding the combined work rate of multiple workers?

Back

The combined work rate is the sum of individual rates. If Tim, JaQuii, and Damien can paint the field in 8, 6, and 4 hours respectively, their rates are 1/8, 1/6, and 1/4. Combined rate = 1/8 + 1/6 + 1/4.

Front

Back

Front

What is the significance of vertical asymptotes in rational functions?

Back

Vertical asymptotes occur where the denominator is zero and the function approaches infinity. They indicate values of x that the function cannot take.

Front

What is the difference between a hole and a vertical asymptote in a rational function?

Back

A hole occurs when a factor cancels out in both the numerator and denominator, while a vertical asymptote occurs when the denominator is zero but the numerator is not.