3. Functions

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. g(x) = (1/2)∛(x-2)

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

g(x) = -f(x) +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 quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. h(x) = -2(x+2)²+1

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

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

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

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)

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

g(x) = ½ f(x)

In Exercises 64–66, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x + 3)

Use the graph of y = f(x) to graph each function g. g(x) = f(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|+3