Rational and Exponential Functions Review

This video covers the final part of the Grade 12 Advanced Functions exam review, focusing on logarithmic and exponential functions, solving equations, graphing reciprocal functions, and analyzing rational inequalities. It provides methods for converting between exponential and logarithmic forms, solving equations with unknowns in exponents, and graphing functions with asymptotes. The video also addresses solving rational inequalities without cross-multiplying and identifying extraneous roots in logarithmic equations.

What is the main focus of the Grade 12 Advanced Functions exam review?

• Logarithmic functions, rational functions, and inequalities

• Geometry and trigonometry

• Statistics and probability

• Basic arithmetic operations

How can you convert an exponential expression to a logarithmic form?

• By subtracting the exponent from the base

• By multiplying the base and the exponent

• By writing the base as the base of the log and the exponent as the result

• By adding the base to the exponent

What is the first step in solving exponential equations with the same base?

• Add the exponents

• Divide the exponents

• Rewrite the powers with the same base

• Multiply the bases

When bases cannot be rewritten, what method is used to solve exponential equations?

• Using the quadratic formula

• Adding the exponents

• Taking the logarithm of both sides

• Cross-multiplying

What must be checked when solving logarithmic equations?

• If the base is greater than 10

• If the argument is a prime number

• For extraneous roots

• If the exponent is negative

What is a key property of reciprocal functions?

• They have a horizontal asymptote at y = 0

• They always pass through the origin

• They have no asymptotes

• They are always increasing

What shape is formed by the graph of the quotient of two linear functions?

• Parabola

• Circle

• Hyperbola

• Ellipse

What should be avoided when solving rational inequalities?

• Using a calculator

• Cross-multiplying

• Factoring the numerator

• Finding common denominators