Function Simplification and Discontinuities

The video tutorial explains how to graph a function by identifying vertical asymptotes and simplifying the function through factoring. It highlights the importance of recognizing points of discontinuity and demonstrates how to graph the function with an open circle at the point of discontinuity. The tutorial concludes with tips on factoring to eliminate discontinuities.

What is the first step in graphing a function according to the video?

• Find the horizontal asymptote

• Identify the vertical asymptote

• Determine the y-intercept

• Calculate the slope

How do you find a vertical asymptote for the function discussed?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Find the derivative

• Integrate the function

Why is it important to simplify a function before graphing?

• To determine the range

• To make calculations easier

• To eliminate unnecessary points

• To find the x-intercept

What is the result of factoring the numerator in the given function?

• A constant function

• A linear equation

• An exponential function

• A quadratic equation

What does the function simplify to after factoring?

• x^2 + 16

• x^2 - 16

• x + 4

• x - 4

What is the final form of the function after simplification?

• x + 4

• x^2 - 16

• x - 4

• x^2 + 16

What is the graphical representation of the simplified function?

• A circle

• A hyperbola

• A straight line

• A parabola

What is the significance of the point x = 4 in the simplified function?

• It is a point of discontinuity

• It is an intercept

• It is a horizontal asymptote

• It is a vertical asymptote

What happens at the point of discontinuity in the graph?

• The graph has a peak

• The graph intersects the x-axis

• The graph is undefined

• The graph has a hole

Why is the point x = 4 not a vertical asymptote in the simplified function?

• Because it is a horizontal asymptote

• Because it is a maximum point

• Because it is an intercept

• Because it is a point of discontinuity