Key Features of Graphs

Identifying Key Features of a Graph

Math 2

EQ: Monday, April 29, 2024

• What are the key features of a graph?

Name the Family of Functions
● Linear
● Exponential
● Quadratic
● Absolute Value
● Piecewise (or Step)
give names of its pieces

Name the Family of Functions
● Linear
● Exponential
● Quadratic
● Absolute Value
● Piecewise (or Step)
give names of its pieces

• A Line

Name the Family of Functions
● Linear
● Exponential
● Quadratic
● Absolute Value
● Piecewise (or Step)
give names of its pieces

• A Line

• Curves up or down

Name the Family of Functions
● Linear
● Exponential
● Quadratic
● Absolute Value
● Piecewise (or Step)
give names of its pieces

• A Line

• Curves up or down

• U-Shaped

Name the Family of Functions
● Linear
● Exponential
● Quadratic
● Absolute Value
● Piecewise (or Step)
give names of its pieces

• A Line

• Curves up or down

• U-Shaped

• V-Shaped

Name the Family of Functions
● Linear
● Exponential
● Quadratic
● Absolute Value
● Piecewise (or Step)
give names of its pieces

• A Line

• Curves up or down

• U-Shaped

• V-Shaped

• Pieces of above

Match

Match the following functions.

Exponential

Quadratic

Absolute Value

Piecewise

Linear

• Exponential

• Quadratic

• Absolute Value

• Piecewise

• Linear

​Vertex

Math Response

Give the y-intercept of the graph.

Type answer here

Correct Answer: 4

Deg^°

Rad

Math Response

Give the x-intercept of the graph.

Type answer here

Correct Answer: -2

Deg^°

Rad

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (for piecewise functions)
● vertex

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (for piecewise functions)
● vertex

​Where graph crosses x-axis

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (for piecewise functions)
● vertex

​Where graph crosses x-axis

​Where graph crosses y-axis

Multiple Choice

Does this graph have a maximum or a minimum?

• Maximum

• Minimum

​This graph does not have a minimum because it keeps going down to negative infinity.

Multiple Choice

Does this graph have a maximum or a minimum?

• Maximum

• Minimum

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (for piecewise functions)
● vertex

​Where graph crosses x-axis

​Where graph crosses y-axis

Lowest point

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (x-value for piecewise functions)
● vertex

​Where graph crosses x-axis

​Where graph crosses y-axis

Lowest point

Highest point

Math Response

Give the Point of Transition.

Type answer here

Correct Answer: 2

Deg^°

Rad

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (for piecewise functions)
● vertex

​Where graph crosses x-axis

​Where graph crosses y-axis

Lowest point

Highest point

The x-value when the graph changes

Points of Interest
● x-intercept(s)
● y-intercept
● minimum
● maximum
● transition points (for piecewise functions)
● vertex

​Where graph crosses x-axis

​Where graph crosses y-axis

Lowest point

Highest point

The x-value when the graph changes

Where the graph turns around

​Axis of Symmetry

○ quadratics
○ absolute value

​Where y is trying to get to when x goes far to the left or right.

Multiple Choice

When x is going FAR to the LEFT where is the y trying to get to?

• 0

• -2

• negative infinity

• 4

Multiple Choice

When x is going FAR to the Right where is the y trying to get to?

• Positive Infinity

• -2

• Negative Infinity

• 4

● Domain

○ What are the vertical boundaries of the graph?

● Range

○ What are the horizontal boundaries of the graph?

Multiple Choice

Give the Domain of the graph.

• $$-6\le x\le6$$

  or

  $$\left[-6,6\right]$$

• $$0<x<6$$

  or

  $$\left[0,6\right]$$

• Negative Infinity

  or

  Positive Infinity

Multiple Choice

Give the Range of the graph.

• $$-6\le x\le6$$

  or

  $$\left[-6,6\right]$$

• $$0<x<6$$

  or

  $$\left[0,6\right]$$

• Negative Infinity

  or

  Positive Infinity

​Domain: -6 < x < 6

​Domain: -6 < x < 6

Range: 0 < y < 6

Multiple Choice

Give the Interval where the graph is Increasing.

• $$\left(-\infty,2\right)$$

• $$\left(4,+\infty\right)$$

• $$\left(-\infty,+\infty\right)$$

Multiple Choice

Give the Interval where the graph is Decreasing.

• $$\left(-\infty,2\right)$$

• $$\left(4,+\infty\right)$$

• $$\left(-\infty,+\infty\right)$$

​The slope of the line or the slope between 2 points of the graph.

Multiple Choice

Give the Average Rate of Change from x = -4 and x = 2.

• 2

• -2

• -8

• -4

Multiple Choice

Give the Average Rate of Change from x = -1 and x = 0.

• 2

• 5

• -4

• 1

​Linear

​Linear

as x goes to -inf y goes to -inf
as x goes to +inf y goes to +inf

​Linear

as x goes to -inf y goes to -inf
as x goes to +inf y goes to +inf

Domain: (-inf, +inf)
Range: (-inf, +inf)

​Linear

as x goes to -inf y goes to -inf
as x goes to +inf y goes to +inf

Domain: (-inf, +inf)
Range: (-inf, +inf)

x-intercept (2,0)
y-intercept (0,-4)

​None

​None

​None

​None

​None

m = 2

​None

​None

m = 2

y = 2x - 4

Graph B
Name the Family of Functions

End Behavior

Domain and Range

Linear Function y = mx + b

Far to the left, y goes to positive infinity

Far to the right, y goes to negative infinity

Domain: (−∞, +∞)
Range: (−∞, +∞)