Identify the effect on the graph of replacing f (x) by f (x) + k, k·f (x), f (kx), and f (x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and explain the effects on the graph, using technology as appropriate. Extend from linear to quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 23, edited]

Example Problems
Seth is collecting data on his height over the years.
Seth has created a
scatter plot that shows the relationship between his height, , and the number of years, . He thinks the data might show a linear relationship.

What graph will show a
linear relationship if Seth's data is indeed linear?
Charles is collecting data on how many grapes his sister eats each day.
Charles has created a
scatter plot that shows the relationship between the number of grapes his sister has eaten, , and the number of days, . He thinks the data might show a linear relationship.

What graph will show a
linear relationship if Charles's data is indeed linear?
Ivy is dropping small steel balls from rest and is collecting data on how far they fall over time.

Ivy has created a scatter plot that shows the relationship between the distance fallen,
, and the time, . She thinks the data might show that is a quadratic function of .

What graph will show a
linear relationship if is indeed a quadratic function?
Goblins

1-on-1 AI tutoring aligned to 8A.25. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →