FUNCTIONS & their Graphs
This shows the different type of Functions and their graphs. For example in y=Cos(x) it shows the direction of the graph.
Point-Slope Form-
In point-slope form it tells you the slope and the point. Once you have those two things you can then graph it. You graph it by plotting the point first. Then you use the slope to do rise/run.
Point slope form is also called as point - gradient form. Point Slope Form is used to generate the Equation of a straight line passing through a given point with a slope.
Remember;
Point slope form = y - y1 = m(x- x1)
Remember;
Point slope form = y - y1 = m(x- x1)
SLOPE
•You just have to remember that when you’re going to find the Slope you have to remember that the Rise is Positive (+) and the Run is Positive (+). So the M is going to be positive as well.
The Slope is basically a surface of which one end or side is at a higher level than another. Like seen in the picture located at the bottom.
To find the slope m of the line segment joining the points, use the slope formula:
Slope-Intercept
Y=mx+b
*The equation is called the slope intercept form for a line.
*The Graph of this equation is a straight line.
*The Slope of the line is m.
*The line crosses the y-axis at b.
*The point where the line crosses the y-axis is called the y-intercept.
*The (x,y) coordinates for the y-intercept are (o,b)
*The Graph of this equation is a straight line.
*The Slope of the line is m.
*The line crosses the y-axis at b.
*The point where the line crosses the y-axis is called the y-intercept.
*The (x,y) coordinates for the y-intercept are (o,b)
Domain
All the values that go into a function
The output values are called the range.
Example: if the function f(x) = x2 is given the values x = {1,2,3,...} then {1,2,3,...} is the domain
The output values are called the range.
Example: if the function f(x) = x2 is given the values x = {1,2,3,...} then {1,2,3,...} is the domain
Range
The difference between the lowest and highest values.
Ragne is the Input of the function.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 = 6.
Ragne is the Input of the function.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 = 6.
For example; The highest number is 6 and the lowest number is - 2, so the range is:
6 - (-2) = 6 + 2 = 8
6 - (-2) = 6 + 2 = 8
Continuity
A function is continuous if you can trace it without lifting your pencil from the paper.
A function may be continuous at some points, and discontinuous at others (continuity is a point-wise property of a function).
A function may be continuous at some points, and discontinuous at others (continuity is a point-wise property of a function).