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, you can modify its equation by scaling the independent variable, which in this case is x.
For the function f(x) = x^3, if you want to stretch it horizontally by a factor of five, you need to stretch the x-values by dividing them by five. The equation of the stretched function would be:
f(x) = (x/5)^3
This means that each x-value from the original function is divided by 5, effectively stretching it horizontally.
Similarly, you can stretch the square root of x by a factor of four. The function for the square root of x is f(x) = √x. To stretch it horizontally by a factor of four, you need to scale the x-values by dividing them by four. The equation of the stretched function would be:
f(x) = √(x/4)
Again, this means that each x-value from the original function is divided by 4, stretching it horizontally.
By applying these transformations, you can stretch any function horizontally by a desired factor.