How do you change the function f(x)=x^3 so that it is stretched horizontally by a factor of five? What about strethching the square root of x by a factor of four? Thanks everyone.
To stretch a function horizontally by a factor of five, we need to modify the input value (x) in the function f(x) = x^3.
Let's call the stretched function g(x). To stretch the function horizontally by a factor of five, we divide the input value (x) by five: g(x) = f(x/5) = (x/5)^3.
By dividing x by 5 inside the parentheses, we compress the function horizontally, making it appear stretched by a factor of five.
Similarly, let's consider the square root function, f(x) = √x. To stretch this function horizontally by a factor of four, we need to modify the input value (x).
Again, let's call the stretched function g(x). To stretch the function horizontally by a factor of four, we divide the input value (x) by four: g(x) = f(x/4) = √(x/4).
By dividing x by 4 inside the parentheses, we compress the function horizontally, making it appear stretched by a factor of four.
So, to summarize:
- To stretch the function f(x) = x^3 horizontally by a factor of five, use g(x) = (x/5)^3.
- To stretch the function f(x) = √x horizontally by a factor of four, use g(x) = √(x/4).
I hope this explanation helps you! Let me know if you have any further questions.