Understanding Functions and Equations

This video tutorial covers various algebra topics, focusing on solving problems from a standardized test. It includes step-by-step solutions for calculating slopes, factoring quadratics, finding parallel lines, and analyzing exponential functions. The video also addresses domain and range, solving systems of equations, and understanding causation. Each problem is explained in detail, with tips on using calculators for verification.

What is the main focus of the video introduction?

• Factoring expressions

• Solving quadratic equations

• Overview of the problems covered

• Graphing linear functions

How do you find the slope from a table of values?

• By adding all x-values

• By subtracting y-values and dividing by the difference in x-values

• By multiplying all y-values

• By dividing x-values by y-values

What is the factored form of 2x^2 - 25x + 63?

• (2x - 7)(x - 9)

• (x - 7)(2x - 9)

• (x - 9)(2x - 7)

• (2x - 9)(x - 7)

What is the standard form of a line parallel to 8x + 3y = 15 passing through (6, -1)?

• 8x + 3y = 17

• 8x + 3y = 45

• 8x - 3y = 15

• 8x + 3y = -45

What is the value of 'a' in the function h(x) = a * f(x) if f(x) = x?

• 0.8

• 0.5

• 1.5

• 2.0

Which model best represents the sea turtle population data?

• A linear model

• An exponential model with b > 1

• An exponential model with b < 1

• A quadratic model

What is the domain of the graphed linear function?

• -4 ≤ x ≤ 5

• -7 ≤ x ≤ 6

• x < -7

• x > 6

What are the solutions to the equation 3x^2 - 30x - 72 = 0?

• x = -2 and x = 12

• x = 2 and x = -12

• x = -3 and x = 11

• x = 3 and x = -11

Which system of equations represents lines f and g?

• f: y = 1.75x + 2.5, g: y = -4x - 6

• f: y = 2x + 4, g: y = -5x - 9

• f: y = 1.5x + 3, g: y = -3x - 7

• f: y = 1.75x + 3.5, g: y = -4x - 8

What is the rate of change of the linear function shown on the grid?

• 3/4

• 7/9

• -7/9

• -3/4