Question

4. Consider the function f(x)=x^2-4

Part A: Write a function that shifts f(x) left 5 units.

Part B: Write a function that shifts f(x) right 8units.

Part C: Write a function that horizontally stretches f(x) by 1/4 units.

Part D: Write a function that horizontally compresses f(x) by 6 units.

HELP!!!! PLSSSS

Answer 1

Using translation concepts, it is found that the modified functions are:

A. $g(x) = x^2 + 10x + 21$

B. $g(x) = x^2 - 16x + 60$

C. $g(x) = 16x^2 - 4$

D. $g(x) = \frac{x^2 - 4}{6}$

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:

$f(x) = x^2 - 4$

Item a:

For a shift left of 5 units, we have $f(x + 5)$, hence:

$g(x) = f(x + 5) = (x + 5)^2 - 4 = x^2 + 10x + 25 - 4 = x^2 + 10x + 21$

Item b:

For a shift right of 8 units, we have $f(x - 8)$, hence:

$g(x) = f(x - 8) = (x - 8)^2 - 4 = x^2 - 16x + 64 - 4 = x^2 - 16x + 60$

Item c:

For a horizontal stretch by a factor of 1/4, we find $f(4x)$, hence:

$g(x) = f(4x) = (4x)^2 - 4 = 16x^2 - 4$

Item d:

For a vertical compression by a factor of 1/6, we find $\frac{1}{6}f(x)$, hence:

$g(x) = \frac{1}{6}f(x) = \frac{x^2 - 4}{6}$

You can learn more about translation concepts at https://brainly.com/question/4521517