Domain, Range & End Behavior Exit Quiz

What is the domain of the graph?

• $\left(0,\infty_{ }\right)$
  

• 
  

  $\left[0,\infty\right)$

• $\left(-\infty,0\right)$
  

• $\left[0,\infty\right]$
  

Answer explanation

Remember domain is all the x values from left to right. You must use brackets [ around the zero because it is an actual point on the graph that is included in the domain. Any form of $\infty$ should always be surrounded by ) because it is not an actual number.

What is the range of the graph?

• $\left[0,\infty\right)$

• [0,9]

• (-3,3)

• $\left(-\infty,\infty\right)$

Answer explanation

Range goes from lowest y value up to highest y value. If you look at the lowest point on the graph, you can see the there is an arrow in which the graph continues going down gradually forever towards $-\infty$ . If you look at the highest point on the graph, you can see there is arrow in which the graph continues going up forever towards $\infty$ . Keep in mind we always list range lowest to highest. Since $\infty$ is not an actual number, we must surround it by ().

What is the range of the function?

• -7≤x≤6 or [-7, 6]

• -7<x<6 or (-7, 6)

• -8<y<2 or (-8, 2)

• -8≤y≤2 or [-8, 2]

What is the DOMAIN of the function?

• [-7, 6]

• (-7, 6)

• [-8, 2]

• [-7, -8]

Answer explanation

-7 is the x - value located furthest left on any part of the graph and is an actual point on the graph so it must contain [

6 is the x- value located furthest right on any part of the graph and is an actual point on the graph so it must contain ]

What is the RANGE for the following graph?

• (-∞, ∞)

• (-∞, 0]

• [-12, 12]

• [-4, 0]

Answer explanation

Since the lowest y-value on the graph consists of arrows pointing down forever, we say the lowest point is - $\infty$ , while the highest point on the graph is where y is 0 and not an arrow.

Describe the end behavior of the graph.

• x → ∞, y→ ∞ and

  x→ ∞, y→⁻∞

• x → ∞, y→ ∞ and

  x→⁻∞, y→∞

• None of these

• x →∞,y→⁻∞ and

  x→∞, y→⁻∞

Answer explanation

Remember that when we talk about the left side, we say

$as\ x\rightarrow-\infty$
When we talk about the right side of a graph, we say $as\ x\rightarrow\infty$

Describe the end behavior of the graph.

• x → ∞, y→ ∞ and x→∞, y→⁻∞

• x → ∞, y→ ∞ and x→⁻∞, y→∞

• x → ∞, y→ ∞ and x→⁻∞, y→ 0

• x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞

Answer explanation

Remember that when we talk about the left side, we say: $as\ x\rightarrow-\infty$

When we talk about the right side of a graph, we say:

$as\ x\rightarrow\infty$