horizontal stretch by 4 so its wider on g(x)=2(x+3)^4-5
To horizontally stretch a function by a factor of k, you need to replace the variable x with x/k in the function.
For the function g(x) = 2(x+3)^4 - 5, to horizontally stretch it by a factor of 4, we divide x by 4:
g(x/4) = 2((x/4)+3)^4 - 5
This stretched function will be wider than the original g(x) by a factor of 4.
To horizontally stretch the function g(x) = 2(x + 3)^4 - 5 by a factor of 4, you need to divide the inside of the parentheses by 4.
1. Start with the original function: g(x) = 2(x + 3)^4 - 5.
2. Divide the inside of the parentheses, (x + 3), by 4: g(x) = 2((x/4) + (3/4))^4 - 5.
3. Simplify the expression inside the parentheses: g(x) = 2((1/4)x + (3/4))^4 - 5.
4. Expand the expression inside the parentheses by raising it to the fourth power: g(x) = 2((1/4)x + (3/4))^4 - 5.
5. Finally, simplify any further if needed.
To horizontally stretch a function, we need to multiply the input (x-values) by a stretch factor. In this case, the function you provided is g(x) = 2(x + 3)^4 - 5, and you want to horizontally stretch it by a factor of 4.
To achieve this, we replace the variable x with (x/4). Therefore, the horizontally stretched function (let's call it h(x)) will be:
h(x) = g(x/4) = 2((x/4) + 3)^4 - 5
Let's simplify this expression:
h(x) = 2((x/4) + 3)^4 - 5
First, we can simplify (x/4) + 3 as follows:
(x/4) + 3 = (1/4)x + 3
Next, we substitute (1/4)x + 3 back into the equation:
h(x) = 2((1/4)x + 3)^4 - 5
Now, we have the horizontally stretched function h(x) = 2((1/4)x + 3)^4 - 5. This function is four times wider than the original function g(x).