3. Functions

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)-1

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

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

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|

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

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

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

What is the relationship between the graphs of ƒ(x)=|x| and g(x)=|-x|?

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|

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

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