Linear function
What is the linear function and how does its equation look?
It is a mathematical function and its equation is f(x)= kx+n
What is the square function and what is its equation?
Its a parable and its equation it y=ax2+bx+c
What is the equation of the rational function? How does one calculate the zeros and the poles
Equation: f(x)= p(x) : q(x)
Zeros: p(x)=0
Poles:q(x)=0
Which trigonomic functions do we know?
Sinus, Cosinus, Tangens, Cotangens
What do Df and Zf reprisent
Df reprisents the area on the x-axis that the function is present
Zf reprisents the area on the y-axis that the function is present
How do we determine the slope of a linear graph if we have got 2 coordinates (exp. T1 (1,2) and T2 (3,5)?
k=(y2-y1)/(x2-x1)
How do we determine the zeros of a quadratic function and what do those tell us?
By equating y with 0 and calculating ax2+bx+c=0, they tell us the intersection points with the x-axis
How does one calculate the horizontal asymptote?
By dividing p(x) with q(x)
How do we mark the the x-axis?
With pi, 2pi, 3pi,....
How do transitions work?
in brackets
+ tells us how many units left we need to move the function
-tells us how many units right we need to move the function
out of brackets
+ tells us how many units up we need to move the function
- tells us how many units down we need to move the function
What does the intersection of a linear graph with the y-axis represent, how do we calculate it?
It represents the point from which we start drawing the graph and we calculate it by equating x with 0
How do we determine the coordinates of the parable s vertex and what does it tell us? (Equations)
By calculating the p and q coordiantes (List), it tells us the parable s highest or lowest point.
How can we determine the growth and fall intervals of the graph?
By calculating the omen
How do we call the highest and the lowest point on the graph?
They are called the maximum and the minimum
What is Heron"s algorithm? Draw its spreadsheet
Showcase it"s use on the example:
f(x)= 6x3-25x2-24x-5
It"s a way for us to calculate the x-axis interceptions
Zeroes: x1=5
x2=-1/2
x3=-1/3
How do we determine the intersection of 2 linear graphs?
By equating the kx+n parts of the function and calculating the x then puting that x into one of the equations and calculating the y
How can we use the discriminant of a quadratic equation to understand the functions shape and position, what is its equation?
It tells us the amount of zeros or x intersections the graph has. If the discriminant is positive we have 2 intersections, if its 0 we have one intersection and if its negative we have no zeros. The equation is D=b2-4ac
Determine which of these cordinate lies on the graph (paper, d primer)
None of the given cordinates lie on the graph
How do we determine the zeroes for the sinus and cosinus function?
Sinus: x=kPI
Cosinus: x=pi/2 + kpi
What is the inverse function?
How do we calculate it?
Solve this example: y= 3x+5
It"s a function that is mirrored throught the
bisector of odd quadrants. That we calculate by swapping the position of x and y and then isolating the y.
Solution: f-1(x) = (x-5)/3
What is the real life application for linear function?
Trend analysis (growth and decline), understanding if two thing are directly or inversly proportional
What is the real life application for the quadratic function
Solving systems of multiple equations, Optimization of the manufactoring cost, calculating the area of an object
What is the ratiional funtion"s real life application?
Forming telecomunication sistems or electrical circuits, modeling the market average
Which functions are odd and which functions are even?
Odd: Sinus, tangens, cotangens
How do we calculate the angle between 2 graphs?
How does the required equation look like?
By calculating tan phi, papir