3. Functions

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

g(x) = −ƒ( x/2) +1

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

Begin by graphing the standard cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. h(x) = (1/2)(x − 2)³ – 1

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

The graph of y=|x-2| is symmetric with respect to a vertical line. What is the equation of that line?

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

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.

Consider the following nonlinear system. Work Exercises 75 –80 in order.

$y=\mid x-1\mid$

$y=x^2-4$

How is the graph of y = x^2 - 4 obtained by transforming the graph of $y=x^2$?

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

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

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