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Sagot :
Using translation concepts, it is found that the modified functions are:
A. [tex]g(x) = x^2 + 10x + 21[/tex]
B. [tex]g(x) = x^2 - 16x + 60[/tex]
C. [tex]g(x) = 16x^2 - 4[/tex]
D. [tex]g(x) = \frac{x^2 - 4}{6}[/tex]
What is a translation?
- A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function is given by:
[tex]f(x) = x^2 - 4[/tex]
Item a:
For a shift left of 5 units, we have [tex]f(x + 5)[/tex], hence:
[tex]g(x) = f(x + 5) = (x + 5)^2 - 4 = x^2 + 10x + 25 - 4 = x^2 + 10x + 21[/tex]
Item b:
For a shift right of 8 units, we have [tex]f(x - 8)[/tex], hence:
[tex]g(x) = f(x - 8) = (x - 8)^2 - 4 = x^2 - 16x + 64 - 4 = x^2 - 16x + 60[/tex]
Item c:
For a horizontal stretch by a factor of 1/4, we find [tex]f(4x)[/tex], hence:
[tex]g(x) = f(4x) = (4x)^2 - 4 = 16x^2 - 4[/tex]
Item d:
For a vertical compression by a factor of 1/6, we find [tex]\frac{1}{6}f(x)[/tex], hence:
[tex]g(x) = \frac{1}{6}f(x) = \frac{x^2 - 4}{6}[/tex]
You can learn more about translation concepts at https://brainly.com/question/4521517
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