[Algebra II] 1.2 / 1.3 / 1.5

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.