3. Functions

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)

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) - 2

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

Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = -|x + 4| +2

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

g(x) = ½ f(x)

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

g(x) = −ƒ( x/2) +1

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

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

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