3. Functions

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

Graph each function. See Examples 1 and 2. h(x)=|-(1/2)x|

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

g(x) = f(-x)+1

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

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

g(x) = -f(2x) - 1

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=-√(x + 1)

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

Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. See Examples 3 and 4. x²+y²=12

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

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

g(x) = f(-x)

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

g(x) = f(-x)+3

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 square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x+1)