How am I supposed to compress f(x) = |2x| - 3 vertically by a factor of 1/4? Please, will you explain this to me?
same way you do any function. If the result is g(x), then
g(x) = 1/4 * f(x)
= (|2x|-3)/4
= |x/2| - 3/4
To compress a function vertically by a factor of 1/4, you need to multiply the function by 1/4. In this case, you want to compress the function f(x) = |2x| - 3 vertically by a factor of 1/4.
Step 1: Start with the function f(x) = |2x| - 3.
Step 2: Multiply the function by 1/4:
(1/4) * (f(x)) = (1/4) * (|2x| - 3).
Step 3: Simplify the expression inside the parentheses:
(1/4) * (|2x| - 3) = (1/4) * |2x| - (1/4) * 3.
Step 4: Simplify further:
(1/4) * |2x| - (1/4) * 3 = (1/4) * (2|x|) - 3/4.
Step 5: Simplify the expression:
(1/4) * (2|x|) - 3/4 = |x|/2 - 3/4.
Therefore, the compressed function f(x) = |2x| - 3 vertically by a factor of 1/4 is f(x) = |x|/2 - 3/4.
To vertically compress a function by a factor of 1/4, you need to multiply the original function by 1/4. In this case, the original function is f(x) = |2x| - 3.
To compress the function f(x) = |2x| - 3 vertically by a factor of 1/4, follow these steps:
Step 1: Define the original function f(x) = |2x| - 3.
Step 2: Multiply the original function by 1/4 to compress it vertically. The new function, let's call it g(x), can be expressed as g(x) = (1/4) * f(x).
Step 3: Substitute the original function, f(x), into the equation g(x) = (1/4) * f(x).
g(x) = (1/4)(|2x| - 3).
Now, the function g(x) represents the vertically compressed version of f(x) by a factor of 1/4.