Answer:
[tex]g(x) = 8x[/tex]
Step-by-step explanation:
Given:
[tex]f(x) = x[/tex]
[tex]Stretch\ factor = 8[/tex]
Required:
Equation of the new function.
Let the new function be represented by [tex]g(x)[/tex]
The interpretation of this question is that;
[tex]g(x) = f(x * 8)[/tex]
Multiply 8 by x
[tex]g(x) = f(8x)[/tex]
If
[tex]f(x) = x[/tex]
then
[tex]f(8x) = 8 * x[/tex]
Multiply 8 by x
[tex]f(8x) = 8x[/tex]
Recall that
[tex]g(x) = f(8x)[/tex]
Substitute [tex]f(8x) = 8x[/tex] in the above expression
[tex]g(x) = 8x[/tex]
Hence, the equation of the new function when stretched by a factor of 8 is [tex]g(x) = 8x[/tex]
