Algebra Concepts and Techniques

This video provides a comprehensive overview of college algebra, covering topics such as exponents, simplifying expressions, solving linear and quadratic equations, graphing inequalities and functions, understanding complex numbers, and solving systems of equations. It also explores functions and their inverses, offering practical examples and techniques for each concept.

What is the result of dividing x to the fifth power by x squared?

• x to the third power

• x to the seventh power

• x to the second power

• x to the fifth power

When simplifying the expression 5x + 3 + 7x - 4, what is the result?

• 12x - 1

• 2x + 7

• 12x + 1

• 2x - 1

Which method is used to multiply two binomials?

• Division method

• Substitution method

• Distributive method

• FOIL method

What is the absolute value of -3?

• 0

• 6

• -3

• 3

If the absolute value of x is 4, what are the possible values of x?

• Only 4

• 0 and 4

• Only -4

• 4 and -4

What is the solution for x in the equation x^2 - 2x - 35 = 0?

• x = 7 and x = -5

• x = -7 and x = 5

• x = 5 and x = -7

• x = 7 and x = 5

Which method is best for solving the system of equations 2x + y = 5 and 3x - y = 0?

• Elimination

• Graphing

• Substitution

• Matrix Method

What is the value of f(5) if f(x) = 5x + 4?

• 24

• 29

• 25

• 19

How do you find the inverse of the function f(x) = 7x - 5?

• Replace f(x) with y, switch x and y, and solve for y

• Take the reciprocal of the function

• Switch the coefficients of x and the constant

• Multiply the function by -1

What is the result of the composite function f(g(x)) if f(x) = 3x + 5 and g(x) = x^2 - 4?

• 3x^2 - 7

• 3x^2 + 5

• x^2 - 4

• 3x + 5