91Ó°ÊÓ

Function Notation Express the rule in function notation. (For example, the rule "square, then subtract \(5 "\) is expressed as the function \(f(x)=x^{2}-5 .\) ) Add \(1,\) take the square root, then divide by 6

Describing Transformations Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f\) (a) \(-f(x)\) (b) \(\frac{1}{3} f(x)\)

Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$f(x)=5-x, \quad g(x)=x^{2}-3 x$$

Identifying Linear Functions Determine whether the given function is linear. If the function is linear, express the function in the form \(f(x)=a x+b\). $$f(x)=\frac{x+1}{5}$$

A function \(f\) is given. (a) Sketch a graph of \(f .\) (b) Use the graph to find the domain and range of \(f\). $$f(x)=2 x+3$$

Describing Transformations Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f\) (a) \(y=f(x-5)+2\) (b) \(y=f(x+1)-1\)

A function is given. Determine (a) the net change and (b) the average rate of change between the given values of the variable. $$f(x)=3 x-2 ; \quad x=2, x=3$$

Functions in Words Express the function (or rule) in words. $$f(x)=2 x+3$$

Graphing Functions Sketch a graph of the function by first making a table of values. $$g(x)=-(x+1)^{2}$$

Describing Transformations Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f\) (a) \(y=f(x+3)+2\) (b) \(y=f(x-7)-3\)