Understanding Functions and Inequalities

This video tutorial covers the January 2024 Algebra 1 Regents exam, focusing on multiple-choice questions 1 through 24. It provides detailed explanations and solutions for each question, covering topics such as graph interpretation, function definition, linear functions, geometric sequences, exponential growth, simplifying expressions, function shifts, solving equations, percentages, y-intercepts, cost comparison, axis of symmetry, polynomial degree, polynomial products, graph intersections, inequalities, exponent rules, interest calculation, factoring polynomials, unit conversion, polynomial zeros, and range of functions.

What is the primary tool required for the Algebra 1 Regents Exam?

• A compass

• A graphing calculator

• A protractor

• A ruler

Which of the following is a characteristic of a function?

• Multiple x inputs for one y output

• One y output for each x input

• Multiple y outputs for one x input

• No y outputs for any x input

In a linear function, what does the term without an x represent?

• The intercept

• The slope

• The fee

• The rate

What is the common ratio in a geometric sequence?

• The difference between terms

• The product of terms

• The factor multiplied to get the next term

• The sum of terms

Which scenario represents exponential growth?

• The number of people doubling every 5 years

• Earning $20 per hour

• A tree growing 1.5 ft per year

• Adding $10 to a jar each week

What must you do when you have a negative sign in front of a parenthesis?

• Ignore it

• Divide everything inside by -1

• Multiply everything inside by -1

• Add 1 to everything inside

How do you shift a function three units to the left?

• Subtract 3 from the function

• Add 3 to x

• Add 3 to the function

• Subtract 3 from x

What is the first step in solving for a variable?

• Add all terms

• Divide all terms

• Isolate the variable

• Multiply all terms

How do you calculate the percentage of a part over a whole?

• Divide part by whole and multiply by 100

• Multiply part by whole and divide by 100

• Add part to whole and multiply by 100

• Subtract part from whole and divide by 100

What does evaluating a function at a specific point mean?

• Graphing the function

• Substituting the point into the function

• Finding the y-intercept

• Finding the slope