Exploring Domain and Range from Graphs

This video tutorial is the third part of an Algebra 1 lesson focusing on graphs of functions, specifically on finding the domain and range. The instructor explains the concepts of domain and range, using finite, infinite, and complex graph examples. For finite graphs, the domain and range are determined by the graph's endpoints. Infinite graphs require abstract thinking, as they extend indefinitely. Complex graphs may have gaps, requiring special notation. The lesson concludes with homework instructions to reinforce the concepts learned.

What do the terms 'domain' and 'range' refer to in the context of a graph?

• The highest and lowest points on the graph.

• All points where the graph intersects the x-axis and y-axis.

• All y-values and x-values covered by the graph, respectively.

• All x-values and y-values covered by the graph, respectively.

How do you determine the domain of a finite graph with clear endpoints?

• By identifying the leftmost and rightmost x-values.

• By finding the points where the graph intersects the y-axis.

• By calculating the slope of the graph.

• By identifying the highest and lowest y-values.

In the notation for domain, what does the chunk in the middle (e.g., -4 ≤ x ≤ 3) represent?

• The points where the graph intersects the x-axis.

• The slope of the graph.

• The interval of x-values between the smallest and largest values.

• The range of y-values.

When determining the range of a finite graph, what should you be careful about?

• Not to confuse the highest point with the endpoint.

• Not to include the x-values.

• Not to use the same notation as for the domain.

• Not to consider the slope of the graph.

How do you determine the domain of a graph that extends infinitely in both directions?

• By calculating the slope of the graph.

• By building imaginary walls to see if the graph hits all x-values.

• By identifying the leftmost and rightmost x-values.

• By identifying the highest and lowest y-values.

What is the domain of a graph that extends infinitely in both directions?

• All integers.

• All negative numbers.

• All real numbers.

• All positive numbers.

For a graph that extends infinitely upwards but has a finite lower limit, how is the range determined?

• By calculating the slope of the graph.

• By identifying the highest y-value.

• By identifying the lowest y-value and stating all values above it.

• By finding the points where the graph intersects the x-axis.

What is the range of a graph that extends infinitely upwards but has a finite lower limit at y = -2?

• All real numbers.

• All real numbers greater than or equal to -2.

• All real numbers less than or equal to -2.

• All positive numbers.

How do you handle a graph with a gap when determining the domain?

• By calculating the slope of the graph.

• By ignoring the gap and considering all x-values.

• By excluding the x-value where the gap occurs.

• By only considering the y-values.

For a graph with a gap at x = 0, what is the domain?

• All real numbers.

• All negative numbers.

• All real numbers except 0.

• All positive numbers.