Section 1.3 – More on Functions

On the interval [-10, -5]: The maximum value is 9. The minimum value is – and –6 are zeroes of the function. The function is increasing on (-10, -7) The function is decreasing on (-7, -5)

On the interval (-10, 10): An absolute maximum occurs at x = -7 An absolute minimum occurs at x = -5 A relative maximum occurs at x = 2. A relative minimum occurs at x = 4 A relative maximum occurs at x = 6 A relative minimum occurs at x = 9

AVERAGE RATE OF CHANGE OF A FUNCTION If a function is defined on the closed interval [a, b], the average rate of change of the function on the interval [a, b] is: On the interval [-3, 0], the average rate of change is: On the interval [1, 2], the average rate of change is:

On the interval [-3, 4], the average rate of change is: On the interval [6, 9], the average rate of change is:

“Even, Odd, or Neither’ Functions Even Functions Symmetrical wrt Y-AXIS f(-x) = f(x) Odd Functions Symmetrical wrt ORIGIN f(-x) = - f(x)

The “Library” of 10 “Standard” Functions Linear Function Constant FunctionIdentity Function Square Function Cubic Function Quartic Function Square Root Function Reciprocal Function Absolute Value Function *Greatest Integer Function

The Cubic FunctionThe Quartic Function

The Square Root FunctionThe Reciprocal Function

The Absolute Value FunctionThe Greatest Integer Function

The Piecewise Function (a) Find the domain of the function (b) Locate any intercepts. (c) Graph the function. (d)Based on the graph, find the range.

The Piecewise Function (a) Find the domain of the function (b) Locate any intercepts. (c) Graph the function. (d)Based on the graph, find the range.

The Piecewise Function (a) Find the domain of the function (b) Locate any intercepts. (c) Graph the function. (d)Based on the graph, find the range.