Understanding the Range of Functions

The video tutorial explains how to determine the range of various types of functions, including linear, quadratic, cubic, absolute value, and radical functions. It emphasizes the importance of graphing to visualize the range and provides examples for each function type. The tutorial also covers how to calculate the vertex for quadratic functions and discusses the behavior of cubic polynomials. The video concludes with a detailed explanation of graphing radical functions and determining their range.

What is the range of a linear function like y = x + 3?

• Negative three to positive infinity

• Zero to positive infinity

• Negative infinity to positive infinity

• Zero to three

For a quadratic function y = x^2, what is the range?

• Zero to positive infinity

• Negative three to positive infinity

• Negative infinity to positive infinity

• Zero to three

How does the range of y = x^2 - 3 differ from y = x^2?

• It shifts up by 3 units

• It becomes negative infinity to 3

• It shifts down by 3 units

• It is the same

What is the range of a cubic polynomial like y = x^3?

• Negative three to positive infinity

• Zero to positive infinity

• Negative infinity to positive infinity

• Zero to three

What shape does the graph of an absolute value function form?

• A cubic curve

• A straight line

• A parabola

• A V shape

For the absolute value function y = |x| + 3, what is the range?

• Negative infinity to positive infinity

• Negative three to positive infinity

• Three to positive infinity

• Zero to three

How does a negative sign outside the absolute value function affect its graph?

• It opens the graph upward

• It shifts the graph down

• It shifts the graph up

• It opens the graph downward

What is the range of the function y = √x?

• Zero to three

• Negative three to positive infinity

• Negative infinity to positive infinity

• Zero to positive infinity

How does the graph of y = √(-x) differ from y = √x?

• It reflects over the x-axis

• It reflects over the y-axis

• It shifts up

• It shifts down

What is the range of the function y = -√(x-3) + 4?

• Negative infinity to positive infinity

• Negative infinity to four

• Zero to positive infinity

• Three to positive infinity