Exploring Parent Functions and Their Characteristics

The video tutorial by Mark from Math Guides covers various parent functions, including constant, linear, absolute value, quadratic, square root, cubic, cube root, exponential, logarithmic, rational, and trigonometric functions. Each function is explained with its characteristics, graph shapes, and transformations. The tutorial emphasizes the importance of understanding these functions for solving real-world problems and mathematical scenarios.

What is the defining characteristic of a constant function?

• The Y value changes constantly.

• The Y value remains constant throughout the graph.

• The function forms a parabola.

• The X value remains constant throughout the graph.

In the linear function y = mx + b, what does 'm' represent?

• The constant term

• The slope

• The x-intercept

• The y-intercept

What shape does the graph of an absolute value function typically have?

• A U-shape

• A V-shape

• A straight line

• A circle

What is the general form of a quadratic function?

• f(x) = √x

• f(x) = x^2

• f(x) = x

• f(x) = |x|

Why does the square root function only have one branch?

• Because it is not defined for negative values.

• Because it is a linear function.

• Because it is its own inverse.

• Because it has a horizontal asymptote.

What is the relationship between cubic and cube root functions?

• They are not related.

• They are inverses of each other.

• They are both linear functions.

• They have the same graph.

What is a key property of an exponential function?

• It is its own inverse.

• It forms a V-shape.

• It has a horizontal asymptote.

• It has a vertical asymptote.

What is the general form of a logarithmic function?

• f(x) = x^2

• f(x) = b^x

• f(x) = 1/x

• f(x) = log_b(x)

What is the defining feature of a rational function?

• It forms a U-shape.

• It has a horizontal asymptote.

• It is defined as f(x) = 1/x.

• It has a constant value.

What is the maximum value of a basic sine function?

• 0

• 1

• 2

• -1