Exploring Parent Functions and Their Characteristics

This video tutorial covers major parent functions, including constant, linear, quadratic, cubic, absolute value, square root, reciprocal, exponential, and logarithmic functions. Each function is explained with its equation, graph, domain, and range. The video emphasizes understanding the characteristics of these functions to aid in transformations and graphing.

What is the graph of a constant function?

• A vertical line

• A horizontal line

• A diagonal line

• A parabolic curve

What is the range of a constant function f(x) = 5?

• y < 5

• y > 5

• y = 5

• All real numbers

In a linear function f(x) = x, what is the relationship between x and y?

• x is the square of y

• x is always greater than y

• x is always less than y

• x is equal to y

What is the shape of the graph of a quadratic function?

• A straight line

• A V-shape

• A parabola

• A cubic curve

What is the domain of a cubic function?

• x ≠ 0

• All real numbers

• x < 0

• x > 0

How does the graph of an absolute value function differ from a quadratic function?

• It is a straight line

• It has a sharp V-shape

• It is a cubic curve

• It is a horizontal line

What is the domain of a square root function?

• x > 0

• x ≥ 0

• All real numbers

• x < 0

What is a key characteristic of a reciprocal function's graph?

• It is a V-shape

• It is a straight line

• It has a parabola shape

• It has asymptotes

What is the range of an exponential growth function?

• y > 0

• y ≥ 0

• All real numbers

• y < 0

How is a logarithmic function related to an exponential function?

• It is the reciprocal of the exponential function

• It is the inverse of the exponential function

• It is the derivative of the exponential function

• It is the square of the exponential function