Graph Behavior and Intercepts

The video tutorial explains the Intermediate Value Theorem, emphasizing its application in finding zeros of polynomials. It describes how a continuous graph ensures that all y-values between two points are covered without lifting the pen. The tutorial further illustrates how to identify x-intercepts by observing changes in y-values from positive to negative or vice versa, using graphical representation and analysis.

What does the Intermediate Value Theorem imply about a continuous graph?

• It only covers positive Y values.

• It skips certain Y values.

• It covers all Y values between two points.

• It has breaks and gaps.

What is a characteristic of a continuous graph?

• You can draw it without lifting your pen.

• It only exists in theory.

• It has multiple breaks.

• It is always a straight line.

What does a continuous graph ensure about Y values?

• They are all zero.

• All Y values between two points are covered.

• They are all negative.

• They are all positive.

What is the role of the Intermediate Value Theorem in graph analysis?

• To calculate the area under the curve.

• To find the highest point.

• To determine the slope.

• To ensure all Y values between two points are covered.

How is the Intermediate Value Theorem used in polynomials?

• To calculate the area under the curve.

• To find zeros or roots.

• To determine the slope.

• To find the maximum value.

What does a transition from positive to negative Y values indicate on a graph?

• A peak point.

• A zero or x-intercept.

• A constant slope.

• A vertical line.

What happens to the graph between x = -1 and x = 0?

• It forms a loop.

• It remains constant.

• It becomes a vertical line.

• It crosses the x-axis.

What does a change from positive to negative Y values signify?

• A zero or x-intercept.

• A peak.

• A constant slope.

• A vertical line.

What must occur between two x-coordinates if a graph goes from positive to negative?

• A constant function.

• A vertical asymptote.

• A horizontal line.

• A zero or x-intercept.

What is indicated by a graph going from negative to positive Y values?

• A horizontal line.

• A zero or x-intercept.

• A maximum point.

• A minimum point.