Answer:
1. shift right by 3.1 units
2. flip over y axis
3. shift up by 1
Step-by-step explanation:
to transform from x⁵ to (-x+3.1)⁵+1, we must do the following
1. add 3.1 to x (plug (3.1 + x) in for x) to get (x+3.1)⁵
2. switch x to -x to get (-x+3.1)⁵
3. add 1 to the remaining function to get (-x+3.1)⁵ +1
1.
f(x) = x⁵
plug (3.1 + x) in for x
f(x+c) is when (x+c) is plugged in to x, and its shifts the graph to the right by c units
here, 3.1 = c
thus, we shift right by 3.1 units to get to (x+3.1)⁵
2.
f(x) = (x+3.1)⁵
f(-x) flips a graph over the y axis, and that's what we're doing as we're switching x to -x, resulting in (-x+3.1)⁵
3.
f(x) = (-x+3.1)⁵
here, we add 1 to the whole function, and not to x. if we plugged it into x, we'd have (-(x+1)+3.1)⁵, which is not what we want. thus, we add 1 to f(x)
f(x) + c shifts a graph up by c units. here, c = 1, so we shift up by 1 to get
(-x+3.1)⁵ + 1
