Stretches and Shrinks of Shapes and Functions
On this web page you will investigate how graphs can be
stretched or shrunk by changing their equations. This exploration will
reinforce
the concepts in Lesson 4.6 of Discovering Advanced
Algebra: An Investigative Approach.
Sketch
This sketch shows a green polygon and its stretch or
shrink by
the scale factor 0.5, colored blue. You can change the scale factor by
dragging point P.
Investigate
 What happens when you change the value of the scale
factor P?
 What happens when P equals zero? When P
equals 1?
 What happens when P
is greater than 1?
Sketch
This sketch shows the graph of the function . Sliders
allow you to change the values of a
and b.
Investigate
 What values of a give a vertical stretch? A
vertical shrink?
 How does the graph differ if a is positive
or negative? Equal to 0?
 How does the graph differ when a
is between 0 and 1?
 Summarize your findings about the effect of
coefficient a on the graph.
 What values of b give a horizontal stretch?
A horizontal shrink?
 How does the graph differ if b is positive
or negative? Equal to 0?
 How can you describe the graph when b
is between 0 and 1?
 Summarize your findings about the effect of
coefficient b on the graph.
 What happens when a
is 2 and b
is 3? Explain.
 If a
is 3, can you find a value of b
that results in the same graph as that of ? Explain.
Sketch
This sketch shows the graph of the function .
Sliders allow you to
change the values of a, b, and c.
Investigate
 What values of a give a vertical stretch? A
vertical shrink?
 How does the graph differ if a is positive
or negative? Equal to 0?
 How does the graph differ when a
is between 0 and 1?
 Summarize your findings about the effect of
coefficient a on the graph.
 What values of b give a horizontal stretch?
A horizontal shrink?
 How does the graph differ if b is positive
or negative? Equal to 0?
 How does the graph differ when b
is between 0 and 1?
 Summarize your findings about the effect of
coefficient b on the graph.
 What does the graph look like when a is 2
and b
is 3? Explain.
 If a is 4, can you find a value of b
that results in the same graph as that of y = x^{2}?
Explain.
 Now change c. What does the graph look like
when c
is positive? Negative? Equal to 0? Explain.
 Can you find values of a, b, and c
that make the graph pass through all three points (0, 3), (2, 1), and
(???4, ???5)? Describe your approach.
Sketch
This sketch shows the graph of the function
and
sliders that allow you to change
the values of a, b, and c.
Investigate
 What values of a give a vertical stretch? A
vertical shrink?
 How does the graph differ if a is positive
or negative? Equal to 0?
 How does the graph differ when a
is between 0 and 1?
 Summarize your findings about the effect of
coefficient a on the graph.
 What values of b give a horizontal stretch?
A horizontal shrink?
 How does the graph differ if b is positive
or negative? Equal to 0?
 How does the graph differ when b
is between 0 and 1?
 Summarize your findings about the effect of
coefficient b on the graph.
 What does the graph look like when a is 2
and b
is 3? Explain.
 Now change c. What does the graph look like
when c
is positive? Negative? Equal to 0? Explain.
 Summarize what you have learned about stretching and
shrinking graphs
vertically and horizontally.
