Understanding Inequalities and Functions

This video tutorial covers a range of mathematical topics, starting with quadratic equations and inequalities, including a review of the quadratic formula and its application to complex solutions. It then moves on to solving exponential and logarithmic equations, with practical examples using Desmos. The tutorial also explains end behavior and points of discontinuity in graphs. Finally, it introduces basic statistics concepts, focusing on sampling methods and population studies.

What is the first step in solving an absolute value inequality?

• Use the quadratic formula

• Isolate the variable

• Isolate the absolute value

• Graph the inequality

When graphing the solution to an absolute value inequality, what does the shaded region represent?

• The solutions that are imaginary

• The solutions that are equal to zero

• The solutions that satisfy the inequality

• The solutions that do not satisfy the inequality

What is the quadratic formula used for?

• Solving exponential equations

• Solving quadratic equations

• Solving linear equations

• Solving logarithmic equations

What should you do if you encounter a negative number under the square root in the quadratic formula?

• Use a different formula

• Ignore it

• Use the absolute value

• Introduce an imaginary unit 'i'

How do you solve a logarithmic equation using Desmos?

• Graph the equation and find the intersection

• Use the quadratic formula

• Use the exponential function

• Use the absolute value function

What is the monthly rate if the annual rate is 1.20?

• 1.53%

• 1.20%

• 2.00%

• 0.20%

Which of the following exponential functions is increasing?

• -5 * 0.5^x

• -3 * 2^x

• 4 * e^x

• 2 * 0.25^x

What is the population in 2008 if the equation is Y = 7^(x + 5) and x is the number of years since 2005?

• 7^3

• 7^8

• 7^10

• 7^5

What causes a point of discontinuity in a function?

• A zero in the numerator

• A negative exponent

• A zero in the denominator

• An imaginary number

What is the right end behavior of a graph that opens upward?

• X goes to zero

• X goes to negative infinity

• Y goes to positive infinity

• Y goes to negative infinity