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

Yulia 2020-11-09 Answered
Explain why the basic transformations of the parent function y=x5 will only generate functions that can be written in the form y=a(x  h)5 + k
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timbalemX
Answered 2020-11-10 Author has 108 answers

Sterp 1
When y=f(x) is stretched vertically by a factor of a, we get the graph for y=af(x)
When y=f(x) is compressed vertically by a factor ofa, we get the graph for y=af(x)
beg{array}{|c|}hleWhen y=x5 is stretched/compressed vertically by a factor of a, we get the graph for y=ax5hleend{array} 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(mx)
beg{array}{|c|}hleWhen y=x5 is stretched horizontally by factor of m, we get the graph for y=m5x5hleend{array}
Which is the same as a vertical shift by a factor a=m5
Therefore, by vertical and horizontal stretch of y=x5 we can obtain the polynomial y=ax5
Step 2 When y=f(x) is reflected across the x-axis, we get the graph for y= f(x)
beg{array}{|c|}hleWhen y=x5 is refleced across the x-axis, we get the graph for y= x5hleend{array}
When y=f(x) is reflected across the y-axis, we get the graph for y=f(x)
beg{array}{|c|}hleWhen y=x5 is refleced across the x-axis, we get the graph for y= x5= x5hleend{array}
Note that sign of a accounts for the reflection about x and y axes
Step 3
When

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