Exponential Functions and Rational Expressions

This video tutorial is designed for students preparing for their pre-calculus final exam. It covers a range of topics including solving exponential equations, evaluating inverse functions, and working with logarithmic expressions. The video also delves into piecewise functions, finding polynomial zeros, and graphing functions with a focus on identifying asymptotes. The tutorial provides step-by-step solutions and encourages students to pause and attempt problems independently before reviewing the solutions.

What is the first step in solving an exponential equation where the bases are different?

• Subtract the exponents

• Convert the bases to a common base

• Divide the bases

• Add the exponents together

How do you find the inverse of a function f(x) = 8/(x-3)?

• Square both sides

• Multiply by the reciprocal

• Switch x and y, then solve for y

• Add 3 to both sides

What is the result of log base 27 of 1/3?

• 3

• -1/3

• 1/3

• -3

How do you determine which part of a piecewise function to use?

• Use the part that is first in the list

• Use the part with the highest degree

• Use the part that matches the x-value condition

• Use the part with the smallest coefficient

What is the formula for continuous compounding interest?

• A = P(1 + rt)

• A = P(1 + r/n)^(nt)

• A = Pe^(rt)

• A = P(1 - rt)

What is the sum of the zeros of the polynomial x^3 - 3x^2 - 10x + 24?

• 6

• 3

• -3

• 0

What must be true for the inside of a square root function to ensure it is real?

• It must be positive

• It must be negative

• It must be zero

• It must be an integer

How do you determine the domain of a rational function?

• Use only positive x-values

• Set the denominator equal to zero and solve

• Set the numerator equal to zero

• Find the highest power of x

What is the horizontal asymptote of the function y = 2^(x+3) + 1?

• y = 0

• y = 2

• y = 1

• y = 3

What is the range of the function y = -|x+2| + 3?

• (-∞, ∞)

• [3, ∞)

• (-∞, 3]

• [0, 3]