1.5 – library of functions Goal: to recognize basic shapes/properties of graphs of different types...
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Transcript of 1.5 – library of functions Goal: to recognize basic shapes/properties of graphs of different types...
1.5 – library of functionsGoal: to recognize basic shapes/properties of graphs of different types of functions
We know many functions and their properties already…
Let’s remember and refer to their parent functionsLinear function: f(x) = x or f(x) = cQuadratic function(squaring): f(x) = x2
Cubic function: f(x) = x3
Radical function(square root): f(x) = Rational function(reciprical): f(x) =
*all the graphs and their properties are defined starting on page 52.
Piecewise-defined functionsLet’s graph the function we evaluated in section 1.3…
𝑓 (𝑥 )={ 𝑥2+2 ,𝑥<272≤𝑥 ≤42𝑥−4 ,𝑥>4
On your own, please graph:
𝑓 (𝑥 )={2𝑥+3 , 𝑥≤1− 𝑥+4 ,𝑥>1
Let’s graph one more…
𝑓 (𝑥 )={2𝑥 ,(−∞,−1)2 𝑥2 ,¿−𝑥+3 ,(2 ,∞)
HOMEWORK:
pg. 56 #’s 3,43, 45, 47, 49, 67, 68
*finish warm up problems too!
Let’s recall the “subway problem”….
What did the graph look like?
Does anyone remember the data?
This graph is called a STEP FUNCTION
The most common step function is the GREATEST INTEGER FUNCTION
*means the greatest integer less than or equal to x
Evaluating the Greatest integer function…
=? =?
=?
=?
= ? =?
Let’s practice evaluating and graphing greatest integer functions…
+1 for f(-1, 2, 1.5,
Partner Work:
Complete Packet
Now please try # 30, 32 on page 56
Homework: Day 2
Pg. 56 #’s 7, 31, 33, 35, 39, 41, 53-62, 63, 66