6A Domain & Range of Quadratic Functions

​6A: determine the domain and range of quadratic functions and represent the domain and range using inequalities

​DOMAIN: all possible x-values; LEFT (least) to RIGHT (greatest)
RANGE: all possible y-values; BOTTOM (least) to TOP (greatest)

Domain: -∞ < x < ∞ , or all real numbers​

​Range: y ≥ 4, or all real numbers greater than or equal to 4

​INEQUALITY Symbols
< means LESS than
> means GREATER than
≤ means LESS than or EQUAL to
≥ means GREATER than or EQUAL to

INFINITY
-∞ negative infinity
∞ positive infinity

Multiple Choice

Which graph best represents a quadratic function with a range of all real numbers greater than or equal to 3?

Multiple Choice

The graph of quadratic function f is shown on the grid.

Which of these best represents the domain of f?

• -3 ≤ x ≤ 2

• all real numbers

• y ≥ -5.5

• All real numbers less than -3 or greater than 2

Drag and Drop

A quadratic function is graphed on the grid.

The domain of the function is ​

Placeholder

.

The range of the function is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

all real numbers

y ≥ 5

y > 5

x ≥ -3

x > -3

x < -3

x ≤ -3

y ≤ 5

y < 5

Multiple Choice

Which graph represents a function with a range of all real numbers greater than or equal to -6?

Multiple Choice

A golfer hit a golf ball from a tee box that is 6 yards above the ground. The graph shows the height in yards of the golf ball above the ground as a quadratic function of x, the horizontal distance in yards of the golf ball from the tee box.

What is the domain of the function for this situation?

• 0 ≤ x ≤ 230

• 6 ≤ x ≤ 230

• 0 ≤ y ≤ 230

• 6 ≤ y ≤ 36

Drag and Drop

The graph of function f is shown on the grid.

The domain of f is ​

Placeholder

.

The range of f is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

all real numbers

all real numbers less than or equal to 0

all real numbers greater than or equal to 0

all real numbers greater than or equal to -3

all real numbers less than or equal to -3

Multiple Choice

The graph of quadratic function f is shown on the grid.

Which of these best represents the range of f?

• y ≥ -5.5

• y > -5.5

• y < -5.5

• y ≤ -5.5

​

​

​

​When part of a function is graphed showing dots instead of arrows, use inequalities to represent domain and range accordingly:

​OPEN dot:
<
>

​CLOSED dot:
≤
≥

​DOMAIN:
-3 < x ≤ 2
All real numbers greater than -3 and less than or equal to 2

​

​RANGE:
3 ≤ y < 12
All real numbers greater than or equal to 3 and less than 12

​DOMAIN:
x < 2
All real numbers less than 2

​RANGE:
y ≤ 4
All real numbers less than or equal to 4

​

Multiple Choice

Part of a quadratic function is graphed on the grid.

Which answer choice best represents the domain and range of the function?

• Domain: x > 1

  Range: y ≤ 9

• Domain: x < 1

  Range: y ≥ 9

• Domain: x ≥ 1

  Range: y ≤ 9

• Domain: x ≥ 1

  Range: y < 9

• Domain: x > 1

  Range: y < 9

Multiple Choice

Which graph best represents part of a quadratic function with a domain of all real numbers less than -4?

Multiple Choice

Which graph represents a domain of all real numbers greater than or equal to -7 and less than 2?