For certain functions (and only those!), there is a relationship between stretching along the y-axis and shrinking along the x-axis and vice-versa. Let's consider the function f(x) = x². (a) Write the equation of f(x) x2 stretched vertically by a factor of m. (b) Write the equation of f(x) = x² stretched horizontally by a factor of n. (c) In order to have the functions in parts (a) and (b) be the same, what does n have to equal in terms of m? (d) Therefore, we can say that vertically stretching y = x² by a factor of m is the same as horizontally stretching y = x? by what amount?
For certain functions (and only those!), there is a relationship between stretching along the y-axis and shrinking along the x-axis and vice-versa. Let's consider the function f(x) = x². (a) Write the equation of f(x) x2 stretched vertically by a factor of m. (b) Write the equation of f(x) = x² stretched horizontally by a factor of n. (c) In order to have the functions in parts (a) and (b) be the same, what does n have to equal in terms of m? (d) Therefore, we can say that vertically stretching y = x² by a factor of m is the same as horizontally stretching y = x? by what amount?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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refer to image. please do C and D
Transcribed Image Text:For certain functions (and only those!), there is a relationship between stretching along
the y-axis and shrinking along the x-axis and vice-versa. Let's consider the function
f(x) = x?.
(a) Write the equation of f(x) = x² stretched vertically by a factor of m.
(b) Write the equation of f(x) = x² stretched horizontally by a factor of n.
(c) In order to have the functions in parts (a) and (b) be the
to equal in terms of m?
same,
what does n have
(d) Therefore, we can say that vertically stretching y
same as horizontally stretching y = x² by what amount?
x² by a factor of m is the
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