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Linear Function
A function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
Linear Equations
Equations that represent linear functions, typically in the form Ax + By = C, where A, B, and C are constants.
Nonlinear Function
Curved line on a raph, can’t be written in f(x) = mx + b, but can be written in Ax + By = C
Intercept
Where a graph of a function intercepts an axis
x / y-intercept
Is the x/y coordinate of a point where the graph intercepts the x/y axis
Line Symmetry
A graph has line symettry if it can be equally reflected on a vertical line
Line of Symmetry
The line splitting a graph into equal halves
Point Symmetry
When a graph is rotated 180 degrees about a point and it maps onto itself
Point of Symmetry
The point that fulfills point symmetry
Even Function
Has line symmetry with y axis (vertical)
Odd Function
Has point symmetry
How to test for an even or odd function algebraically
Replace all x with (-x), if result from the powers is the same then its even, if not, it’s odd
How does x —> (-x) decide a if a function is even or odd
If the x power is even it’s positive, if not it’s odd, if the negative(d) equation is the same as the original it is an even function, if it is opposite it is an odd function, if it is different then its neither.
Extrema
The maximum and minimum values of a function
Maximum
The highest point on the graph of a function
Minimum
The lowest point on the graph of a function
Relative Maximum
High peak points where there is no other nearby high points
Relative Minimum
Point on the graph where no other nearby points have a lesser y-coordinate
End Behaviour
The behaviour of a graph as x approaches positive or negative infinity
What does: As X —> -oo, f (x) —> -oo mean?
It means that as the function moves left on the x axis, it will also go down on the y axis
What does: As x —> +oo, f(x) —> +oo mean?
As the function moves right on the x axis, it will go up on the y axis
The equation for graphing on a calculator is
Y = mX + b
In order to check the table version of a graph you must
2nd + graph
Why is the table version of a graph important
Because we can use the values to plot the graph manually on paper
How to graph using y / x- intercept
First, use the equation with all x values being 0, get the y-intercept, plot it.
Then, re-write the equation with all y values being 0, get the x-intercept, plot it.
Finally, connect the dots.
How to graph using slope intercept form
Plot the y intercept, then plot the nearest point with the slope and connect
Linear Inequality
Equation using >, <, >_, <_
>_, <_
Continous Line (Closed half-plane)
>, <
Dashed Line (Open half-plane)
Boundary
The graphed line of an inequality
What happens when an inequality is multipled or divided by a negative value
The inequality signs are flipped
What must be done after an inequality boundary is drawn
The side that applies to it must be shaded
How do we figure out which side gets shaded
Use any point (0,0), and apply it’s number to the x and y values, if the inequality is true (9 > 0) logically, then that side is shaded and the other isn’t.
