Understanding Linear Functions and Graphs

The video tutorial explains how to graph piecewise functions by breaking down the process into three main expressions, each with specific constraints. The instructor demonstrates how to convert these expressions into the y=mx+b form, identify slopes and intercepts, and apply constraints to graph each segment accurately. The tutorial emphasizes understanding the constraints and how they affect the graphing of each piece of the function.

What is a piecewise function?

• A function with a single linear equation.

• A function defined by multiple sub-functions, each with its own domain.

• A function that only has a quadratic equation.

• A function that is always continuous.

Why do piecewise functions have constraints?

• To make them continuous.

• To ensure they are always increasing.

• To limit the domain of each sub-function.

• To make them easier to graph.

What is the purpose of rewriting expressions in y = mx + b form?

• To find the roots of the equation.

• To identify the slope and y-intercept.

• To convert them into quadratic form.

• To make them easier to integrate.

What is the y-intercept of the expression y = -1?

• 1

• 0

• -1

• 2

What is the slope of the expression y = 2x?

• 0

• 1

• 2

• -2

How do you determine the slope from the equation y = mx + b?

• By looking at the value of m.

• By looking at the value of b.

• By looking at the value of x.

• By looking at the value of y.

What is the significance of the y-intercept in a graph?

• It is where the line crosses the y-axis.

• It determines the domain.

• It determines the slope.

• It is where the line crosses the x-axis.

What is the significance of the slope in a graph?

• It determines the range.

• It determines the domain.

• It determines the y-intercept.

• It determines the steepness of the line.

How do you graph a line with no slope?

• As a curved line.

• As a diagonal line.

• As a horizontal line.

• As a vertical line.

What does a closed circle on a graph indicate?

• The line is discontinuous.

• The point is included.

• The point is not included.

• The line is continuous.