3. Functions

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

The green dotted curve below is a graph of the function $f\(\left\)(x\(\right\))$. Find the domain and range of $g\(\left\)(x\(\right\))$(the blue solid curve), which is a transformation of $f\(\left\)(x\(\right\))$.

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

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

g(x) = f(x-1)

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

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