1. Reflecting the graph of y = f(x) across the y-axis using the transformation y = f(-x) does not change the range of the graph, which remains [-5, 1]. 2. The order of transformations can matter. For example, reflecting a graph across the x-axis before translating it up 4 units results in a different graph than if the transformations were performed in reverse order.

1. 1. The range of the graph of y = f(x) is [-5, 1].
Explain why there is no effect on the range of the
graph that is a result of the transformation y = f(-x).
2. Does the order that the transformations are performed matter?
For example, a reflection in the x-axis and a translation of 4 units
up. Show an example to justify your answer.

2. Sum and Differences of Functions
Combined functions can be formed by adding or
subtracting two or more functions.
The sum of two or more functions can be found by
adding the y-coordinates of the functions.
h(x) = (f + g)x
h(x) = f(x) + g(x)
Ex. If f(x) = 2x + 3 and g(x) = x - x - 5, find h(x) = (f + g)x

3. Similarly, the difference of two or more functions can
by found by subtracting the y-coordinates of the functions.
h(x) = (f - g)x
h(x) = f(x) - g(x)
Ex. If f(x) = 2x + 3 and g(x) = x - x - 5, find h(x) = (f - g)x

4. + 3 and g(x) = -2(x+1)

5. Products and Quotients of Functions
of two functions f(x) and g(x) is represented by
h(x) = (f • g)(x)
h(x) = f(x)g(x)
quotient of two functions f(x) and g(x) is represented by
h(x) =( )
h(x) = f(x)