Characteristics of a Graph

Key Features of Graphs

Domain

The set of all possible inputs of a function

Range

The set of all possible outputs of a function.

Multiple Choice

Find the domain and range of the graph shown

• domain (-infinity, infinity) range: (-infinity, infinity)

• domain (-infinity, infinity) range [-1]

• (3,-1)

• (4, -1)

Multiple Choice

_{What is the domain and range of the graph shown?}

• domain: [-2,2] range: [-4, 4]

• domain: (-infinity, infinity) range: (-infinity, infinity)

• (0,1)

• not possible

Multiple Choice

What is the range of the graph?

• 1 ≤ x ≤ 5
• 1 < x < 5
• 1 ≤ y ≤ 5
• 1 < y < 5

Multiple Choice

Which function has a range y ≥ -4?

• None of the above

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D:{-4, 0, 1, 2}
  R:{-4, -3, 1}
• D:{0, 1, 2, 3, 4}
  R:{1, -3, -4}

Rate of Change and Slope

• The rate of change is a comparison between two quantities that are changing. Slope is often used to describe a rate of change

• Slope is a measure of the steepness of a line, which represents its rate of change

• Parallel lines have the same slope

• Perpendicular Lines have opposite reciprocal slopes.

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

Find the slope

• 4/5
• 5/4
• -5/4
• -4/5

Multiple Choice

Find the slope of the line.

• -2
• 2
• -1
• 1

Multiple Choice

How do you know your slope is positive?

• It is constant

• It is increasing

• It is decreasing

• I don't know

Multiple Choice

Find the rate

• 1/2

• (0,0)

• (2,1)

• -1/2

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2
• -2

Y-Intercept

The y-coordinate(s) of the graph, where the graph intersects the y-axis.

Multiple Choice

What is the y-intercept of the graph?

• No solution

• (2,0)

• (0,2)

• (1,0)

Multiple Choice

_{What is the y-intercept of the line?}

• y = 1/2
• y = 1
• y = -1/2
• y = -1

Multiple Choice

Give the y-intercept

• (2,0)
• (0,2)
• (0,-2)
• there is no y-intercept

Multiple Choice

What is the y-intercept?

• (0,7)
• (0,0)
• (1,9)
• (2,11)

Multiple Choice

_{What is the y-intercept of the line?}

• (-1,0)
• (-1,-3)
• (1,1)
• (0-1)

Multiple Choice

What is the y-intercept?

• (6, 0)
• (0, 6)
• (-3, 0)
• (0, -3)

X-intercept

The x-coordinate(s) of a graph, where the graph intersects the x=axis.

Zero of a Function

Graphically, the zero(s) are the x-coordinates of the point(s) where the graph crosses the x-axis. These are also called the root(s) of the function.

Multiple Choice

What are the green dots called?

• y-intercepts
• maximum
• minimum
• roots/x-intercepts

Multiple Choice

What is the x-intercept?

• (12,0)
• (0,-3)
• (8,-1)
• (0,0)

Multiple Choice

^{What is the x- intercept of the line?}

• x = 1
• x = 2
• x = -1
• x = -2

Multiple Choice

^{What is the x- intercept of the line?}

• (0,-1)
• (-2,0)
• (-1,0)
• (0,-2)

Multiple Choice

What is the x-intercept for the given graph?

• 1
• -2
• 2
• 1/2

Multiple Choice

What are the zero(s) of this equation?

• (0,1) , (0,2)

• (1,0) , (2,0)

• (0,1) , (2,0)

• (1,0) , (0,2)

Multiple Choice

What are the roots of the function?

• 3

• -6

• -1 and -3

• -6, -1, and -3

Multiple Select

What are the zeroes of the function?

• All real numbers

• -1

• 5

• -2

• -4

Multiple Choice

Name the x-intercept(s)?

• 0
• 4
• 2
• 0 and 4

Axis of Symmetry

The vertical line that divides a parabola into two symmetric halves.

Fill in the Blanks

Multiple Choice

What is the equation of the axis of symmetry?

• y = 0

• x = 0

• x = 3

• x = -3

Vertex

The point that lies on the axis of symmetry of a parabola. This is the highest or lowest point and the y-value is called the maximum or the minimum

Multiple Choice

What is the vertex of the graph?

• x=3

• y=2

• (2,3)

• (3,2)

Multiple Choice

What is the minimum?

• None
• (0,4)
• (3,1)
• y = -1

Multiple Choice

What is the vertex?

• (-3, 0)

• (3, 0)

• (0, 18)

• (18, 0)

Multiple Choice

Which statement about the graph is FALSE?

• The vertex is (-3, 18)

• The vertex is a maximum

• The y-intercept is y = 0

• The axis of symmetry is y = -3

Multiple Choice

What is the significance of the ordered pair (1, -2) to the graph?

• It is the maximum point

• It is the vertex

• It is the y-intercept

• It is an x-intercept

Multiple Choice

Which function has a maximum of 0?

Multiple Choice

Does this graph in the back have maximum or minimum value?

• maximum

• minimum

• neither

• both