Comparing Functions: Key Concepts and Techniques

Why is it helpful to use graphs on the same coordinate plane when comparing two functions?

• It makes it easier to see the differences in their rates of change.

• It allows for more colorful graphs.

• It helps in solving equations faster.

• It reduces the number of calculations needed.

What is the first step in graphing a function described in words?

• Guessing the shape of the graph.

• Finding and plotting the given points.

• Drawing a random line.

• Using a calculator to find the slope.

When graphing a function using an input-output table, what values should you choose for x?

• A mix of negative, zero, and positive numbers.

• Only zero.

• Only negative numbers.

• Only positive numbers.

What does a steeper line on a graph indicate about the rate of change?

• It changes slower.

• It changes faster.

• It remains constant.

• It has no change.

What shape is a parabola that opens downwards?

• A U shape.

• A straight line.

• An upside-down U shape.

• A circle.

How do you describe the behavior of a parabola for x greater than zero?

• Y is increasing.

• Y is decreasing.

• Y remains constant.

• Y is undefined.

When comparing two functions, why is it important to find exact points where the graph crosses?

• To ensure the graph is colorful.

• To avoid using a ruler.

• To accurately compare their rates of change.

• To make the graph look symmetrical.

What should you do if a function's equation includes a fraction?

• Ignore the fraction.

• Choose x-values that simplify the fraction.

• Only use positive x-values.

• Graph it without any calculations.

What is the significance of parallel lines on a graph?

• One changes faster than the other.

• They have the same rate of change.

• They intersect at some point.

• They have different rates of change.

What should you do if you are confused about any part of the notes?

• Skip the confusing parts.

• Guess the answers.

• Rewatch the notes and ask questions in class.

• Ignore the confusion.