Functions and Linear Relationships

Vin guides viewers through the August 2022 Algebra 1 Regents exam, covering topics such as function evaluation, common ratios, difference of squares, solving equations, distributive property, graph analysis, data representation, linear functions, quadratic equations, recursive sequences, unit conversion, domain analysis, correlation, and solving for variables. The video provides step-by-step solutions and tips for using calculators effectively.

What is the value of f(8) for the function f(x) = (3x + 4) / 2?

• 18

• 12

• 16

• 14

What is the common ratio of the sequence where the first two terms are x and 2x^2?

• x^2

• 2x^2

• 2x

• x

Which value of x would make the relation a function if the x-values are -4, 3, and -1?

• -4

• 3

• -1

• 4

What is the result of distributing 1/3 in the expression 1/3(6x^2 - 3x + 9)?

• 2x^2 - x + 3

• 2x^3 - x^2 + 3x

• 2x^2 - x^2 + 3

• 2x^2 - x + 3x

Which polynomial function has zeros at x = 2 and x = -3?

• x^2 + 5x + 6

• x^2 + x - 6

• x^2 - x - 6

• x^2 - 5x + 6

What is the constant term in the polynomial 3x^3 + 2x^2 + 7x + 6?

• 3

• 6

• 2

• 7

Which situation can be modeled by a linear function?

• A car's value decreases by 7% annually.

• A gym charges a $50 initial fee and $30 per month.

• An investment grows by 5% annually.

• Bacteria in a lab doubles weekly.

What is the y-intercept of the function y = sqrt(x - 3) when x = 0?

• 3

• 1

• 0

• -3

What is the value of a_4 in the recursive sequence defined by a_n = 3a_(n-1) + 1, with a_1 = -2?

• -41

• -14

• -5

• -42

Which set of calculations converts 1500 meters in 15.42 minutes to miles per hour?

• 1500 / 3.281 / 5280 * 60 / 15.42

• 1500 / 3.281 * 5280 / 60 * 15.42

• 1500 * 3.281 / 5280 * 60 / 15.42

• 1500 * 3.281 * 5280 / 60 / 15.42