Rational Functions and Exponential Concepts

This video tutorial provides a comprehensive review of key Algebra 2 concepts, including simplifying fractions, operations with fractions, solving rational equations, understanding asymptotes, composite functions, inverses, logarithms, exponential growth and decay, and conics. The instructor explains each topic with examples, highlighting important strategies and potential pitfalls. The video also covers the use of calculators for logarithmic calculations and provides insights into the properties of conics, such as circles, ellipses, and hyperbolas.

What is the first step in simplifying a fraction?

• Factor the numerator and denominator

• Multiply the denominators

• Add the numerators

• Subtract the exponents

When multiplying fractions with variables, what do you do with the exponents?

• Divide them

• Add them

• Subtract them

• Multiply them

What must be true about the denominators when adding fractions?

• They must be less than 10

• They must be greater than the numerators

• They must be prime numbers

• They must be equal

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

• A solution that satisfies the equation

• A solution that does not satisfy the original equation

• A solution that is always positive

• A solution that is always zero

What causes a vertical asymptote in a rational function?

• A zero in the denominator

• A positive exponent

• A zero in the numerator

• A negative exponent

How do you find the inverse of a function?

• Add 1 to the function

• Multiply the function by -1

• Divide the function by 2

• Switch the x and y variables

What indicates exponential growth in a function?

• A base greater than 1

• A base less than 1

• A negative exponent

• A positive exponent

What is the general form of the equation of a circle?

• x^2 + y^2 = r^2

• x^2 - y^2 = r^2

• x^2 + y = r^2

• x + y^2 = r^2