Ch. 1.1.3: Which Values Are Possible? Domain & Range.

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Ch : Which Values Are Possible? Domain & Range

a) If f(x)= √x, what is f(−16)? Not possible, cannot square root a negative number. b) Domain: collection of numbers that are possible inputs for the function (i.e. possible x-values) What numbers are in the domain of f(x) = √x ? Any negative value will not be in the domain Domain are all positive numbers and zero Domain written as x≥0 c) If g(x) = −(x−2) 2, what is x when g(x) = 11? Not possible, all outputs from this eqn will be negative. d) Range: set of all possible values that can be outputs of a function (i.e. possible y-values) What else is a part of the range of g(x) = −(x−2) 2 ? No positive values will be in the range Range is all negative numbers and zero Range written as y≤0

Draw a complete graph of y = (x + 1)(x − 9). a) Describe the graph completely. Include: x-intercepts: (−1,0) & (9,0) y-intercepts: (0,−9) vertex: (4,−25) On graph paper! b) What window in your calculator lets you see the whole graph? Example: x-min= −5y-min= −30 x-max= 12y-max= 10 c) How do window settings help you describe domain & range? They include key points and allow you to see where graphs end or if they continue to infinity.

Draw a complete graph of y = (x − 12) a) What happens when you use standard window? You cannot see the graph, it’s not visible. b) What window settings should you use to see enough of the graph to visualize and draw a complete graph? Example: x-min= −5y-min= −5 x-max= 20y-max = 30 c) What are the domain & range of the function? Domain: All Real Numbers  written as Range: All Real Numbers Greater Than & Equal To 11  written as y≥11

Reverse thinking & create a graph w/ given D & R a) Sketch a function w/ D: All Real #’s between & including −3 and 10 (written as −3 ≤ x ≤ 10) R: All Real #’s between & including −4 and 6 (written as −4 ≤ y ≤ 6) b) Sketch a function w/ D: x > −3 R: All Real #’s Examples??

Find the solution to the system of eqns: 5x − y = 35 3x + y = −3 a) Graph both eqns on your graphing calculator. MUST GET IN Y= FORM FIRST!! Can you see the solution (intersection point) in the standard window? b) Change the window so you can see the solution. What did you change it to? Example: x-min= −5y-min= −20 x-max= 10y-max= 5 c) “Trace” the graph to find the intersection point. Does it match your algebraic answer? (4,−15)

Finish 1-31 & 1-32 in your teams Check your answer with me before class is out! Homework: Ch.1(34-40, skip 39) DUE 9/9