3. Functions

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 cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. g(x) = x³-3

Describe how the graph of each function can be obtained from the graph of ƒ(x) = |x|. g(x) = -|x|

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

Let ƒ(x) = 3x -4. Find an equation for each reflection of the graph of ƒ(x). across the x-axis

Begin by graphing the standard cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. h(x) = -x³

Let ƒ(x) = 3x -4. Find an equation for each reflection of the graph of ƒ(x). across the y-axis

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.

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

(a) y = ƒ(x) +3

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

(b) y = ƒ(x-2)

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

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

(d) y = |ƒ(x)|

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

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

Begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. g(x) = (1/2)∛(x-2)