College Algebra Final Exam Review – Step-by-Step Guidance

Q2. The graph below shows the percentage of students enrolled in the College of Engineering at Stale University. Use the graph to answer the following:

• a. Does the graph represent a function?

• b. If f represents the function, find f(1995).

• c. If f(x) = 12%, what year is represented by x?

Background

Topic: Functions and Graphs

This question tests your understanding of functions, how to interpret graphs, and how to use function notation to extract information from a graph.

Key Terms:

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

• Function Notation: $f(x)$ represents the output value for a given input $x$.

• Domain: The set of all possible input values (years, in this case).

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

Step-by-Step Guidance

1. To determine if the graph represents a function, check if each year (x-value) corresponds to only one percentage (y-value). This is often called the "vertical line test." If any vertical line crosses the graph more than once, it is not a function.

2. For part (b), locate the year 1995 on the x-axis and find the corresponding y-value (percentage) on the graph. This value is $f(1995)$.

3. For part (c), find the year where the percentage of students enrolled is 12%. Look for the point on the graph where the y-value is 12%, and identify the corresponding x-value (year).

Try solving on your own before revealing the answer!

Final Answer:

• a. Yes, the graph represents a function because each year corresponds to only one percentage.

• b. $f(1995) = 20\%$ (from the graph).

• c. $f(x) = 12\%$ corresponds to the year $x = 1985$.

Each part uses the graph to match input (year) to output (percentage), demonstrating function concepts.