3. Functions

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=-3(x-2)²+1

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

Work each problem. Find a function g(x)=ax+b whose graph can be obtained by translating the graph of ƒ(x)=2x+5 up 2 units and to the left 3 units.

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

Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (-4, -2)

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. g(x)=(x+2)²

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

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

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

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

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