Algebraic Expressions and Functions

The video tutorial covers various algebra topics, including causal relationships, function analysis, linear equations, exponential and polynomial expressions, statistics, sequences, quadratic functions, interest rates, and recursive sequences. The instructor uses real-world examples and calculator techniques to explain concepts, providing a comprehensive understanding of algebraic principles.

Which of the following scenarios represents a causal relationship?

• The more gasoline you buy, the more you pay.

• The longer a shopper stays at the mall, the more purchases they make.

• The more minutes an athlete plays, the more goals they score.

• As the price of a gift increases, the size of the gift box increases.

What is the correct value of f(3) for the function f(x) = 3x - 5?

• 7

• 4

• 10

• 0

What is the fixed cost in the equation for the cost of a salad with additional toppings?

• $0.50

• $2.00

• $5.75

• $0.75

Which expression is equivalent to x^2 + 5x - 6?

• (x + 6)(x - 1)

• (x + 3)(x - 2)

• (x + 6)(x - 1)

• (x - 6)(x + 1)

What inequality represents the situation where Peter spends on lemonade and juice boxes?

• 2x + 0.5y < 100

• 2x + 0.5y > 100

• 2x + 0.5y ≥ 100

• 2x + 0.5y ≤ 100

Which type of numbers is most appropriate for the domain of a function representing days in January?

• Rational numbers

• Whole numbers

• Integers

• Real numbers

Which table of values represents an exponential relationship?

• x: 1, 2, 3; y: 3, 6, 9

• x: 1, 2, 3; y: 5, 10, 15

• x: 1, 2, 3; y: 4, 16, 64

• x: 1, 2, 3; y: 10, 7.5, 5

Which expression is not equivalent to 5^(2x*3)?

• 5^(3x*2)

• 5^(6x)

• 5^(5x)

• 5^(2*3x)

Which relation is a function?

• x: 1, 2, 2; y: 3, 4, 5

• x: 1, 2, 3; y: 3, 3, 3

• x: 1, 2, 3; y: 3, 4, 5

• x: 1, 1, 1; y: 3, 4, 5

What are the zeros of the function f(x) = (2x - 4)(3x + 4)?

• x = -4, x = 2/3

• x = 4, x = -2/3

• x = -2, x = 4/3

• x = 2, x = -4/3