what is the horizontal stretch by 4 of g(x) = 2(x+3)^4 - 5
The horizontal stretch by a factor of 4 of the function g(x) = 2(x+3)^4 - 5 can be done by dividing the x-values by 4.
To find the new function, we substitute x/4 for x in the original function:
g(x/4) = 2((x/4) + 3)^4 - 5
This simplifies to:
g(x/4) = 2((x+12)/4)^4 - 5
Further simplifying:
g(x/4) = 2((x+12)^4)/4^4 - 5
g(x/4) = 2(x+12)^4/256 - 5
Therefore, the horizontal stretch by 4 of g(x) = 2(x+3)^4 - 5 is g(x/4) = 2(x+12)^4/256 - 5.
To find the horizontal stretch of the function g(x) = 2(x + 3)^4 - 5 by a factor of 4, you need to divide the x-values by 4. The equation for the horizontally stretched function, let's call it f(x), is:
f(x) = 2((x/4) + 3)^4 - 5
Let's break down the steps:
Step 1: Divide the x-values by 4.
Replace "x" with "(x/4)" in the original function:
g(x) = 2((x/4) + 3)^4 - 5
Step 2: Simplify the expression.
Distribute the 2 to the terms inside the parentheses:
g(x) = 2(x/4 + 3)^4 - 5
Simplify the expression inside the parentheses:
g(x) = 2((x + 12)/4)^4 - 5
Simplify further:
g(x) = 2(x + 12)^4/4^4 - 5
Step 3: Simplify the expression completely.
Simplify the term 4^4:
g(x) = 2(x + 12)^4/256 - 5
So, the horizontally stretched function is f(x) = 2(x + 12)^4/256 - 5.
To determine the horizontal stretch of a function, we need to look at the coefficient in front of the function's argument inside the parentheses.
In the given function, g(x) = 2(x+3)^4 - 5, the function inside the parentheses is (x+3). The coefficient in front of (x+3) is 2.
If we want to find the horizontal stretch factor, we take the reciprocal of this coefficient. In this case, the reciprocal of 2 is 1/2.
Therefore, the function g(x) = 2(x+3)^4 - 5 is horizontally stretched by 4.