Domain and Range: Graph

Domain-

Look horizontally: What x-values are contained in the graph? That’s your domain!Range-

Look vertically: What y-values are contained in the graph? That’s your range!

Domain and Range: Graph

Domain: [-3,2]

Range: [-5, 2]

Domain and Range: Graph

Domain: [-3,3)

Range: (-1, 2]

Maximum and Minimum

Maximum value: the highest y value seen in the data or on the graph.

Minimum value: the lowest y value seen in the data or on the graph.

Max and Min: Graph

Max: 2

Min: -5

Zeros: Graph

Zeros: -3; -1.2; 2

Increasing and Decreasing: Graph

To find where the graph is increasing and decreasing trace the graph with your finger from left to right. Specify x-values!

If your finger is going up, the graph is increasing.

If your finger is going down, the graph is decreasing.

Increasing and Decreasing

Inc: (-3,-2.1); (.9,2.1)

Dec: (-2.1,.9)

Increasing and Decreasing

∞-∞

: ( , .5)Dec

: ( .5, )Inc

End Behavior: Graph

The value a function, f(x), approaches when x is extremely large (∞) (to the right) or when x is extremely small (-∞) (to the left).

End Behavior

, ( )

, ( )

x f x

x f x

End Behavior

, ( )

, ( )

x f x

x f x

Points of Discontinuity• These are the points where the function either “jumps” up or

down or where the function has a “hole”.

• For example, in a previous example

Has a point of discontinuity at

x=1

The step function also has points of discontinuity at x=1, x=2 and x=3.

Maxima and Minima(aka extrema)

In this function, the minimum is at y = 1

In this function, the minimum is at y = -2

Highest point on the graph

Lowest point on the graph

Axis of Symmetry• The vertical line that splits the equation in

half.

For the equation the axis of symmetry is located at x = 1

1 1y x

This ‘axis of symmetry’ can be found by identifying the x-coordinate of the vertex (h,k), so the equation for the axis of symmetry would be x = h.

Intervals of Increase and Decrease• By looking at the graph of a piecewise

function, we can also see where its slope is increasing (uphill), where its slope is decreasing (downhill) and where it is constant (straight line). We use the domain to define the ‘interval’.

This function is decreasing on the interval x < -2, is Increasing on the interval -2 < x < 1, and constant over x > 1