Intermediate Algebra Midterm Review Guidance

Q17. Use the vertical line test to determine whether the graph is the graph of a function.

Background

Topic: Functions and Relations

This question is testing your understanding of the vertical line test, which is used to determine whether a relation is a function by examining its graph.

Key Terms:

• Function: A relation in which each input (x-value) corresponds to exactly one output (y-value).

• Vertical Line Test: If any vertical line crosses the graph more than once, the graph does not represent a function.

Step-by-Step Guidance

1. Examine the graph provided. Look for places where a vertical line could intersect the graph at more than one point.

2. Recall that for a relation to be a function, each x-value must map to only one y-value. If a vertical line hits two or more points, that x-value has multiple outputs.

3. Apply the vertical line test visually to the graph. Imagine or draw vertical lines at different x-values and observe how many times each line intersects the graph.

Try solving on your own before revealing the answer!

Final Answer: Not a function

The vertical line test shows that some vertical lines intersect the diagram at more than one arrow, indicating multiple outputs for a single input.

Q18. Use the vertical line test to determine whether the graph is the graph of a function.

Background

Topic: Functions and Graphs

This question asks you to use the vertical line test on a graph to determine if it represents a function.

Key Terms:

• Vertical Line Test: A method to check if a graph is a function by seeing if any vertical line crosses the graph more than once.

Step-by-Step Guidance

1. Look at the graph and identify the shape or curve.

2. Imagine drawing vertical lines at various x-values across the graph.

3. Check if any vertical line would intersect the graph at more than one point.

Try solving on your own before revealing the answer!

Final Answer: Function

Every vertical line intersects the graph at most once, so it passes the vertical line test and is a function.

Q19. Find the domain and the range of the relation. Use the vertical line test to determine whether the graph is the graph of a function.

Background

Topic: Domain, Range, and Functions

This question is about identifying the domain and range from a graph and using the vertical line test to determine if the graph represents a function.

Key Terms:

• Domain: The set of all possible input values (x-values).

• Range: The set of all possible output values (y-values).

• Vertical Line Test: Used to check if a graph is a function.

Step-by-Step Guidance

1. Examine the graph and identify the leftmost and rightmost points to determine the domain.

2. Identify the lowest and highest points on the graph to determine the range.

3. Apply the vertical line test by imagining vertical lines at different x-values and checking if any line intersects the graph more than once.

Try solving on your own before revealing the answer!

Final Answer: Domain: [-4, 4], Range: [-3, 3], Not a function

Some vertical lines intersect the ellipse at two points, so it fails the vertical line test and is not a function.