3. Functions

Begin by graphing the standard cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. h(x) = (1/2)(x − 2)³ – 1

The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows.

(c) y = ƒ(x+3) - 2

Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = -2|x+3|+2

Graph each function. See Examples 1 and 2. g(x)=(1/2)x²

Graph each function. See Examples 1 and 2. h(x)=√(4x)

Each of the following graphs is obtained from the graph of ƒ(x)=|x| or g(x)=√x by applying several of the transformations discussed in this section. Describe the transformations and give an equation for the graph.

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. h(x) = (1/2) (x − 1)² – 1

Use the graph of y = f(x) to graph each function g.

g(x) = 2f(x)

Use the graph of y = f(x) to graph each function g. g(x) = f(x+1)

Begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. ∛(-x-2)

Graph each function. See Examples 1 and 2. ƒ(x)=3|x|

What is the relationship between the graphs of ƒ(x)=|x| and g(x)=|-x|?