Function Operations and Transformations

The video tutorial covers various mathematical concepts, including problem-solving techniques for addition, division, multiplication, and subtraction. It delves into complex problem-solving, function composition, and inverses, providing algebraic verification methods. Graphing techniques and translation rules are explained, along with equations of lines and symmetry. The tutorial also includes graph analysis, focusing on domain, range, and behavior such as increasing or decreasing.

What is the result of adding the functions f(x) = -2x^2 + 2x - 1 and g(x) = -3x^2 - 3x - 1?

• -5x^2 - x + 2

• -5x^2 - 5x - 2

• -5x^2 + x - 2

• -5x^2 - x - 2

When dividing functions, what is the recommended assumption about simplification?

• Assume it does not simplify.

• Simplify only if terms are identical.

• Always simplify the fraction.

• Simplify if the numerator is larger.

What does the dot symbol represent in function operations?

• Multiplication

• Division

• Subtraction

• Addition

What is the result of multiplying f(x) = x^2 - 7 and g(x) = x + 5 when x = 2?

• 21

• -21

• -14

• 14

In subtraction of functions, what is crucial to remember when dealing with parentheses?

• Ignore the parentheses.

• Multiply the terms.

• Distribute the negative sign.

• Add the terms directly.

What is the result of foiling (t - 7)^2?

• t^2 + 7t + 49

• t^2 - 7t + 49

• t^2 - 14t + 49

• t^2 + 49

When verifying inverses, what should the composition of f(g(x)) and g(f(x)) result in?

• 0

• 1

• x

• y

What is the first step in finding the inverse of a function?

• Add 1

• Switch x and y

• Divide by 4

• Multiply by 2

What transformation occurs when a function is shifted left by 1 and down by 1?

• x - 1, y + 1

• x + 1, y - 1

• x + 1, y + 1

• x - 1, y - 1

What is the symmetry of a function that is neither even nor odd?

• Both symmetries

• No symmetry

• Origin symmetry

• Y-axis symmetry