Graphing Functions with Key Features of the 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 Blank

What is the equation for the line of symmetry in this graph?

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