Precalculus Day 36

Precalculus Day 36

Precalculus Day 36

Knight’s Charge a. cos(60o) = ____ RA:______ Quad:_____ NO CALCULATOR:   a. cos(60o) = ____ RA:______ Quad:_____ b.sin( 𝜋 4 ) = _____ c. tan(300o) = ___ d. cot( 45o) = ____ e. csc(270o) = ___ f. sec ( 5𝜋 4 ) = _____ g. sin(-150o) = ___ h. tan(𝜋 ) = _____

Domain and Range The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Domain and range can be seen clearly from a graph, as well as from a function.

Domain and Range from a graph domain  x rangey

Domain and Range from a graph domain  x rangey

Domain and Range from a graph domain  x rangey

Domain and Range from a graph domain  x rangey

Increasing/Decreasing Intervals Another way of saying that a graph is going up is that its slope is positive or that the function is INCREASING. If the graph is going down, then the slope will be negative, and we say the function is DECREASING. NOTE: A function that does not have a constant slope can be increasing on a certain interval and decreasing on another interval.

Increasing and Decreasing Intervals Find all relative minima and maxima. 2nd TRACE 3 and 4

Increasing and Decreasing Intervals Describe the increasing and decreasing behavior. The function is decreasing on the interval increasing on the interval

The function is decreasing over the entire real line. Increasing and Decreasing Intervals Describe the increasing and decreasing behavior. The function is decreasing over the entire real line.

Increasing and Decreasing Intervals Describe the increasing and decreasing behavior. The function is increasing on the interval constant on the interval decreasing on the interval

Group Practice Where is each function increasing and decreasing?  

Group Practice

Relative Max and Min

Relative Max and Min

Relative Max and Min

Relative Max and Min

Relative Max and Min

Function Type: Even, Odd, or Neither Even function A function f(x) such that f(x) = f(–x) This means the graph of f(x) will have a line of symmetry at the y-axis

Even Functions

Function Type: Even, Odd, or Neither Even function A function f(x) such that f(x) = f(–x) This means the graph of f(x) will have a line of symmetry at the y-axis Odd function A function f(x) such that f(x) = –f(–x) The means the graph of f(x) will have rotation symmetry about the origin

Function Type: Even, Odd, or Neither

Function Type: Even, Odd, or Neither Even function A function f(x) such that f(x) = f(–x) This means the graph of f(x) will have a line of symmetry at the y-axis Odd function A function f(x) such that f(x) = –f(–x) The means the graph of f(x) will have rotation symmetry about the origin A function can be neither even nor odd

Are the following functions even, odd, or neither?

EvaluAting Functions from Graph