3. Functions

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

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

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

g(x) = ½ f(x)

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

g(x) = −ƒ( x/2) +1

In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x+1)

In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(-x)

In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = 2f(x+2) − 1

In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = -f(x+2)

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

In Exercises 45-52, use the graph of y = f(x) to graph each function g. g(x) = f(x-1) – 1

In Exercises 45-52, use the graph of y = f(x) to graph each function g. g(x) =(1/2) f(2x)

In Exercises 53-66, 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

In Exercises 60–63, begin by graphing the standard quadratic function, f(x) = x^2. Then use transformations of this graph to graph the given function. g(x) = x^2 + 2

In Exercises 67–69, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. r(x) = (1/2) |x + 2|

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

In Exercises 67-80, 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)

In Exercises 67-80, 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)

Consider the following nonlinear system. Work Exercises 75 –80 in order. y = | x - 1 | y = x^2 - 4 How is the graph of y = x^2 - 4 obtained by transforming the graph of y = x^2?

In Exercises 81–94, 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|

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.

In Exercises 95-106, 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

In Exercises 95-106, 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

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.

In Exercises 107-118, begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. -∛(x+2)

In Exercises 107-118, begin by graphing the cube root function, f(x) = ∛x. Then use transformations of this graph to graph the given function. ∛(-x+2)