Given:
The function is [tex]f(x)=3.5x^3[/tex].
To find:
Whether the given function is Steeper, Less steep, or Reflected over the x-axis to describe the other function.
Solution:
Transformation of function: If f(x) is function and
[tex]g(x)=a\ f(x)[/tex]
Here, a is vertical stretch or compression.
If 0<|a|<1, then g(x) is less steeper than f(x) because f(x) is vertically compressed.
If |a|>1, then g(x) is steeper than f(x) because f(x) is vertically stretched.
If a is negative, the f(x) is reflected over the x-axis, to get g(x).
On comparing the function [tex]p(x)=4.5x^3[/tex] with [tex]f(x)=3.5x^3[/tex], we get 4.5>3.5 So, it is the case vertical stretched and p(x) is steeper than f(x).
On comparing the function [tex]q(x)=-x^3[/tex] with [tex]f(x)=3.5x^3[/tex], we get |-1|=1<3.5 So, it is the case vertical compression and q(x) is less steeper than f(x) and because of negative sign the function is reflected over axis.
On comparing the function [tex]r(x)=3x^3[/tex] with [tex]f(x)=3.5x^3[/tex], we get 3<3.5 So, it is the case vertical compression and r(x) is less steeper than f(x).
Therefore, [tex]p(x)=4.5x^3[/tex] is steeper.
[tex]q(x)=-x^3[/tex] is less steep and reflected over the x-axis.
[tex]r(x)=3x^3[/tex] is less steep.
