Answered: "Explain why the basic transformations of the parent..."

College
Algebra
College algebra
Transformations of functions

Yulia

Answered question

2020-11-09

Explain why the basic transformations of the parent function

y = x^{5}

will only generate functions that can be written in the form

y = a {(x - h)}^{5} + k

Answer & Explanation

timbalemX

Skilled2020-11-10Added 108 answers

Sterp 1
When $y = f (x)$ is stretched vertically by a factor of $a,$ we get the graph for $y = a f (x)$
When $y = f (x)$ is compressed vertically by a factor of $a$ , we get the graph for $y = a f (x)$
$b e g \in {a r r a y} {| c |} h l \in e When y = x^{5} is stretched/compressed vertically by a factor of a, we get the graph for y = a x^{5} ∖ h l \in e e n d {a r r a y}$ Note that we can also stretch the graph horizontall,
When $y = f (x)$ is stretched horizontally by a factor of m, we get the graph for $y = f (m x)$
$b e g \in {a r r a y} {| c |} h l \in e When y = x^{5} is stretched horizontally by factor of m, we get the graph for y = m^{5} x^{5} ∖ h l \in e e n d {a r r a y}$
Which is the same as a vertical shift by a factor $a = m^{5}$
Therefore, by vertical and horizontal stretch of $y = x^{5}$ we can obtain the polynomial $y = a x^{5}$
Step 2 When $y = f (x)$ is reflected across the x-axis, we get the graph for $y = - f (x)$
$b e g \in {a r r a y} {| c |} h l \in e When y = x^{5} is refleced across the x-axis, we get the graph for y = - x^{5} ∖ h l \in e e n d {a r r a y}$
When $y = f (x)$ is reflected across the y-axis, we get the graph for $y = f (- x)$
$b e g \in {a r r a y} {| c |} h l \in e When y = x^{5} is refleced across the x-axis, we get the graph for y = - x^{5} = - x^{5} ∖ h l \in e e n d {a r r a y}$
Note that sign of $a$ accounts for the reflection about x and y axes
Step 3
When

Do you have a similar question?Recalculate according to your conditions!

New Questions in College algebra

Didn't find what you were looking for?