The graph of f(x)=cos(x) is transformed to a new function, g(x) , by stretching it horizontally by a factor of 4 and shifting it 1 unit up.
What is the equation of the new function g(x) ?
im so confused :/ please help
f(x) = cos(x/4) + 1
To stretch the graph of f(x) = cos(x) horizontally by a factor of 4, we multiply the x-values by 1/4. This stretches the graph horizontally, making it narrower.
To shift the graph 1 unit up, we add 1 to the y-values.
So, the equation of the new function g(x) is: g(x) = cos(1/4x) + 1.
No problem! Let's break down the process step by step to find the equation of the new function g(x).
1. Start with the original function, f(x) = cos(x).
2. Horizontal Stretch: The graph is stretched horizontally by a factor of 4. To stretch a function horizontally, we need to multiply the x-values by the factor. Therefore, we replace x with x/4 in the original function. Now we have f(x) = cos(x/4).
3. Vertical Shift: The graph is shifted 1 unit up. To shift a function vertically, we simply add or subtract a constant value to the original function. In this case, we add 1 to the previous function. So now we have f(x) = cos(x/4) + 1.
4. Rename the function: The original function f(x) has been transformed into the new function g(x) as per the problem. So we can rewrite the equation as g(x) = cos(x/4) + 1.
Therefore, the equation of the new function g(x) is g(x) = cos(x/4) + 1.