8th Grade Comparing Functions Word Problem Examples

📚 Quick Study Guide

🔍 Functions can be represented in various ways: equations, tables, graphs, and verbal descriptions.

💡 To compare functions, look at their key features like slope (rate of change) and y-intercept (initial value).

📝 When comparing functions represented as equations, identify the slope ($m$) and y-intercept ($b$) in the slope-intercept form: $y = mx + b$.

📊 When comparing functions represented as graphs, visually analyze the steepness (slope) and where the graph crosses the y-axis (y-intercept).

📈 When comparing functions represented as tables, calculate the rate of change between consecutive points and identify the y-intercept (the value of $y$ when $x = 0$).

🗣️ When comparing functions represented as verbal descriptions, carefully extract the information about the rate of change and initial value.

Practice Quiz

1. Which of the following functions has the greatest rate of change?
   1. $y = 3x + 2$
   2. $y = \frac{1}{2}x - 1$
   3. Function represented by the table:

      x	y
      0	1
      1	4

   4. Function represented by the graph of a line passing through (0, -3) and (1, -1).
2. Function A is described by the equation $y = 5x - 3$. Function B is described by the equation $y = 2x + 1$. Which function has a smaller y-intercept?
   1. Function A
   2. Function B
   3. Both have the same y-intercept
   4. Cannot be determined
3. A car rental company A charges a flat fee of $20 plus $0.30 per mile. Company B charges a flat fee of $30 plus $0.20 per mile. Which company is cheaper if you drive 50 miles?
   1. Company A
   2. Company B
   3. Both are the same price
   4. Cannot be determined
4. Function 1: $y = -2x + 5$. Function 2: A line passes through points (0,3) and (1,1). Which function has the steeper slope?
   1. Function 1
   2. Function 2
   3. Both have the same slope
   4. Cannot be determined
5. A lemonade stand sells lemonade for $1.50 per cup. Another stand has the following sales:

   Cups	Revenue
   2	$2.00
   4	$4.00

   Which stand makes more revenue per cup?
   1. The first stand
   2. The second stand
   3. Both make the same revenue
   4. Cannot be determined
6. Function A is represented by $y = 4x - 1$. Function B is represented by the following table:

   x	y
   0	2
   1	5

   Which function has the larger y-intercept?
   1. Function A
   2. Function B
   3. Both have the same y-intercept
   4. Cannot be determined
7. A gym membership at gym A costs $10 per month plus $5 per class. A gym membership at gym B costs $20 per month plus $3 per class. For what number of classes are the total costs the same?
   1. 3 classes
   2. 4 classes
   3. 5 classes
   4. 6 classes