Functions

  y= logx a is a logarithmic function with a= log number and x= log base. y=logx a reads “y is equal to log⁡a base x.” The logarithmic function is only defined if a > 0, a≠1 and x > 0 An exponential equation can be written as a logarithmic...

The inverse of a function takes the y-values (range) of the function to the corresponding x-values (domain) and vice versa. Therefore, the x and y values are interchanged. The function is reflected along the line y=x to form the inverse. The notation for the inverse...

A. Hyperbola of the Form y=a/x or xy=a Hyperbola of the form: y=a/x or xy=a, where a≠0, x≠0, and y≠0. Shape:  The shape of a hyperbola of the form y=a/x or xy=a   Domain: x∈R; x≠ 0 Range: y∈R; y≠ 0 The horizontal asymptote is the x-axis. The vertical...

Table 2.1: Important terms to remember regarding basic functions, formulas, and graphs. Term Definition Domain The set of possible x-values. Range The set of possible y-values. Axis of symmetry An imaginary line that divides a graph into two mirror images of each...

We use function notation f(x) to show that each y-value is a function of an x-value. We can also use other letters, such as g(x), h(x), and so on. So, y= 2x-1 can be written as f(x)=2x-1 The value of f(x) for any x-value can be worked out by substitution: For example,...