Graphing Rational and Radical Equations

Is this a function? What is the domain and range? Use the equation, and the Desmos graphing calculator to approximate to the hundredths if needed (two decimal places).

• yes

  D: (-∞, -3) υ (-3, +∞)

  R: (-∞, 2) υ (2, +∞)

• no

  D: (-∞, -3) υ (-3, +∞)

  R: (-∞, 2) υ (2, +∞)

• yes

  D: (-∞, 2) υ (2, +∞)

  R: (-∞, -3) υ (-3, +∞)

• no

  D: (-∞, 2) υ (2, +∞)

  R: (-∞, -3) υ (-3, +∞)

What are the zeros? What is the y-intercept? Use the equation, and the Desmos graphing calculator to approximate to the hundredths if needed (two decimal places).

• zeros:

  (0, -3.50)

  y-int:

  (2.33, 0)

• zeros:

  (3.50, 0)

  y-int:

  (0, 2.33)

• zeros:

  (2.33, 0)

  y-int:

  (0, -3.50)

• zeros:

  (-3.50, 0)

  y-int:

  (0, 2.33)

What are the critical points? What are the intervals it is increasing or decreasing? Use the equation and the Desmos graphing calculator to approximate any points (two decimal places).

• no critical points

• Relative Min: (0, 2.33)

  Relative Max: (-3.5, 0)

• Increasing

  (-∞, -3)

  Decreasing

  (-3, +∞)

• Increasing:

  none

  Decreasing

  (-∞, -3)

  (-3, +∞)

• Relative Min: (0, 2.33)

  Absolute Max: (-3.5, 0)

Graph analysis.

Describe the continuity.

Use the equation, and the Desmos graphing calculator to approximate to the hundredths if needed (two decimal places).

• continuous

• discontinuous - infinite

  x = -3

• discontinuous - jump

  x = 2

• discontinuous - removal

  x = -3

• 45
• 55/3
• 5
• 189

Which is the graph of the given function

• 
• 
• 
• 

Which of the following is the function shown in the graph?

• y = √(x - 3)

• y = √(x) + 3

• y = √(x + 3)

• y = √(x) - 3

Graph analysis.

Describe the end behavior.

Use the equation and the Desmos graphing calculator to approximate any points (two decimal places).

• x → -∞

  f(x) → 2

• x → -∞

  f(x) → 3

• x → +∞

  f(x) → 2

• x → +∞

  f(x) → 3

Graph analysis.

Describe the symmetry.

Use the equation and the Desmos graphing calculator to approximate any points (two decimal places).

• x-axis symmetry

• y-axis symmetry

• origin symmetry

• none

Graph analysis.

Is it an even or odd function?

Use the equation and the Desmos graphing calculator to approximate any points (two decimal places).

• even

• odd

• neither