Will you explain how to stretch f(x) = |2x| - 3 horizontally by a factor of 3/2?
Certainly! To stretch the function f(x) = |2x| - 3 horizontally by a factor of 3/2, you need to multiply the argument of the function, which in this case is 2x, by the reciprocal of the stretch factor.
So, to stretch the function horizontally by a factor of 3/2, you divide the argument of the function by 3/2.
The stretched function, let's call it g(x), can be found by applying this transformation:
g(x) = f(x / (3/2))
Now, we substitute the original function f(x) = |2x| - 3 into the equation for g(x):
g(x) = |2(x / (3/2))| - 3
Simplifying further:
g(x) = |(2/3) * x| - 3
So, the stretched function is g(x) = |(2/3) * x| - 3.
This means that the original function has been horizontally stretched by a factor of 3/2.
Of course! To stretch a function horizontally by a factor of 3/2, we need to multiply the input values (x-values) by the reciprocal of the stretch factor.
In this case, the original function is f(x) = |2x| - 3. To stretch it horizontally by a factor of 3/2, we will multiply the x-values by the reciprocal, which is 2/3.
To do this, we can create a new function, g(x), where g(x) = f((2/3)x). Let's break down the steps:
Step 1: Start with the original function f(x) = |2x| - 3.
Step 2: Replace the x-values with (2/3)x to create g(x), so g(x) = |2((2/3)x)| - 3.
Step 3: Simplify the equation: g(x) = |(4/3)x| - 3.
Now, the function g(x) represents the function f(x) stretched horizontally by a factor of 3/2.