Final answer:
To determine the domain and range of each given function, we need to apply the given transformations and restrictions. The graph of each function will be derived based on the transformations applied to the original graph of the function. Graphing the functions will help visualize the changes.
Step-by-step explanation:
Determining the domain and range of each function:
a) For the function y=2f(x), the domain remains the same as f(x), which is x ≥ -4, x∈ R. The range is doubled, so it becomes y.
b) For the function y=-2f(-x+5)+1, we need to find the new domain by replacing x with (-x+5) in the original domain. The new domain is -9 ≤ x ≤ 5, x∈ R. The range remains the same as f(x), which is -1 < y ≤ 0, y∈ R.
c) For the function y=3f(x+1)+4, we need to subtract 1 from each value in the original domain to get the new domain. The new domain is -5 ≤ x ≤ 1, x∈ R. The range is multiplied by 3 and then shifted up 4 units, so it becomes y .
d) For the function y=f(-x), we need to replace x with (-x) in the original domain. The new domain is -∞ < x ≤ 4, x∈ R. The range remains the same as f(x), which is y .
Graphing each function:
a) The graph of y=2f(x) will have the same shape as f(x), but the y-values will be doubled.
b) The graph of y=-2f(-x+5)+1 will have the same shape as f(x), but it will be reflected across the y-axis, flipped vertically, shifted 5 units to the right, and shifted 1 unit up.
c) The graph of y=3f(x+1)+4 will have the same shape as f(x), but it will be shifted 1 unit to the left and shifted 4 units up.
d) The graph of y=f(-x) will have the same shape as f(x), but it will be reflected across the y-axis.