Understanding Function Properties and Characteristics

The video tutorial explains the concept of parent functions, focusing on their simplest forms within function families. It covers the quadratic, linear, cubic, square root, and reciprocal functions, discussing their general forms, graphs, and characteristics such as domain, range, symmetry, and intercepts. The tutorial also explains how to determine if a function is increasing, decreasing, or constant, and highlights the importance of understanding parent functions for graphing other functions.

What is a parent function?

• A function that is always increasing

• A function with no real coefficients

• The simplest form of a function family

• The most complex form of a function family

Which of the following is the parent function for the quadratic function family?

• f(x) = 1/x

• f(x) = x^3

• f(x) = x^2

• f(x) = ax^2 + bx + c

What is the domain of the parent function f(x) = x^2?

• Numbers greater than zero

• Only negative numbers

• Only positive numbers

• All real numbers

Which function has a U-shaped graph?

• f(x) = 1/x

• f(x) = x^2

• f(x) = x^3

• f(x) = √x

Which characteristic is NOT typically included when discussing function graphs?

• Symmetry

• Color

• Range

• Domain

For a function to be increasing, what must be true about two points x1 and x2?

• f(x1) must be greater than f(x2)

• x1 must be less than x2 and f(x1) must be less than f(x2)

• x1 must be greater than x2

• f(x1) must equal f(x2)

What is the general form of a linear function?

• f(x) = m(x) + b

• f(x) = ax^2 + bx + c

• f(x) = 1/x

• f(x) = x^3

Which of the following is a characteristic of the identity function?

• It is symmetric about the y-axis

• It is always decreasing

• It is an odd function

• It has no intercepts

What is the y-intercept of the identity function f(x) = x?

• (1, 0)

• (0, 1)

• (1, 1)

• (0, 0)

What is the slope of the identity function f(x) = x?

• -1

• 2

• 1

• 0