Algebra 2 Pre-Unit
Name: _________________________________
Investigation 2 WS
Hour: ________
Date: ______________
1. In high school Matt grew from weighing 95 pounds to 162 pounds. What was Matt’s change in weight during
high school?
2. Sue did poorly on a History test causing her grade to go from 84.1% o 78.3%. What was the change to Sue’s
grade?
3. In winter, the temperatures in northern Wisconsin can be quite cold. When Lauren woke up this morning (6:00
am) the temperature outside was -18°F. When she got home from school (4:00 pm) the temperature outside
was 4°F. What was the change in temperature from 6:00 am to 4:00 pm?
4. Let x and y represent the values of two different quantities.
a. If the value of x changes from 𝑥 = 2 to 𝑥 = 17, what is the change in x?
b. If the value of y changes from 𝑦 = 5 to 𝑦 = −22, what is the change in y?
c. If the value of x changes to 𝑥 = −13 from 𝑥 = −31, what is the change in x?
d. If the value of y changes from 𝑦 = 9 to 𝑦 = 𝑐, what is the change in y?
5. Let x and y represent the values of two different quantities.
a. If the value of x changes from 𝑥 = 12 to 𝑥 = 1, what is the change in x?
b. If the value of y changes from 𝑦 = −8 to 𝑦 = 15, what is the change in y?
c. If the value of x changes to 𝑥 = −19 from 𝑥 = 4, what is the change in x?
d. If the value of y changes from 𝑦 = −3 to 𝑦 = 𝑏, what is the change in y?
6. Fill in the following tables showing the appropriate changes in the variable values.
7. Fill in the following tables showing the appropriate changes in the variable values.
8. Each of the following graphs shows two ordered pairs (𝑥, 𝑦). Find Δ𝑥 and Δ𝑦 from the point on the left to the
point on the right.
9. Each of the following graphs shows two ordered pairs (𝑥, 𝑦). Find Δ𝑥 and Δ𝑦 from the point on the left to the
point on the right.
10. Suppose we start with a value of 𝑥 = 7.
a. What expression represents the change in x from 𝑥 = 7 to any possible value of x?
b. Repeat part (a) if our initial reference value is 𝑥 = 12 instead of 𝑥 = 7.
11. Suppose we start with a value of 𝑥 = −15.
a. What expression represents the change in x from 𝑥 = −15 to any possible value of x?
b. Repeat part (a) if our initial reference value is 𝑥 = −22 instead of 𝑥 = −15.
12. Suppose Lauren bought a puppy. At the time she bought the puppy it weighed 8 pounds. Let w represent the
weight of the puppy in pounds.
a. What is the difference between saying 𝑤 = 12 and Δ𝑤 = 12?
b. If we substitute 𝑤 = 22.4 into the expression 𝑤 − 8, what are we calculating?
c. If we substitute 𝑤 = 31 into the expression 𝑤 − 17, what are we calculating?
13. Think about the idea of the change in a variable from one value to another. What do the following expressions
represent when we substitute a value for the variable?
a. 𝑥 − 1
b. 𝑦 − (−7) or 𝑦 + 7
c. 𝑟 − 18.1
d. 𝑝 − (−4.6) or 𝑝 + 4.6
14. Think about the idea of the change in a variable from one value to another. What do the following expressions
represent when we substitute a value for the variable?
a. 𝑥 − 23
b. 𝑦 − (−6) or 𝑦 + 6
c. 𝑟 − 41.2
d. 𝑝 − (−33.5) or 𝑝 + 33.4