Functions and Equations Concepts

This video tutorial covers exponential functions and equations, including growth and decay models. It provides examples of exponential growth with computer viruses and decay with city populations. The tutorial also delves into solving algebraic expressions, long division, systems of equations, graphing, and intercepts. Additionally, it explores kinetic energy and quadratic equations, offering a comprehensive overview of advanced math concepts relevant to SAT preparation.

What is the primary characteristic of exponential functions?

• They divide by a constant factor each time period.

• They subtract a constant value each time period.

• They multiply by a constant factor each time period.

• They add a constant value each time period.

In the example of computer virus incidents, what was the initial number of incidents in 2007?

• 2014

• 92%

• 247,000

• 2573

How is the rate of decay represented in the exponential decay formula?

• r + 1

• r - 1

• 1 - r

• 1 + r

What is the equivalent expression for x to the -2?

• 1/x^2

• x^2

• x^-1

• x^0

When solving equations with exponents, what must you remember to do after squaring both sides?

• Subtract the exponents.

• Check the solutions for validity.

• Multiply the exponents.

• Add the exponents.

What is the remainder when 6u^2 - u - 4 is divided by 3u - 2?

• -2

• 0

• 2

• -4

In solving rational equations, what is the first step?

• Subtract the numerators.

• Divide by the common denominator.

• Multiply everything by the common denominator.

• Add the denominators.

What is the value of y if x = -3 in the system of equations where y = -3x + 2?

• 6

• -6

• 9

• -9

Which function has x-intercepts at -4 and 5?

• (x - 4)(x - 5)

• (x + 4)(x + 5)

• (x - 4)(x + 5)

• (x + 4)(x - 5)

Which value of k results in a function having four solutions?

• k = 1

• k = 0

• k = -1

• k = -2