A linear function is shown on the graph. a linear function beginning with closed circle at 2 comma 0 and ending with a closed circle at 9 comma 7 What is the domain of the function?
a. {x | 2 < x < 9}
b. {x | 2 ≤ x ≤ 9}
c. {y | 0 < y < 7}
d. {y | 0 ≤ y ≤ 7}
The domain of a linear function is all the possible values of x that correspond to a valid y-value on the graph. In this case, the function begins at x = 2 and ends at x = 9, so the domain must include all values of x between those two points.
However, since the dots at x = 2 and x = 9 are closed circles, this means that they are included in the domain as well (since the function value is defined at those points). Therefore, the correct answer is (b) {x | 2 ≤ x ≤ 9}.
The range of a relation is
the output (y) values of the relation
the input (x) values of the relation
a set of points that pairs input values with output values
x and y values written in the form (x, y)
The range of a relation is the output (y) values of the relation.
Is the following relation a function?
x y
1 −2
1 −3
2 1
3 −2
Yes
No
No, the relation is not a function because the input value x=1 is associated with two different output values y=-2 and y=-3. A function has only one output value for each input value.
A quadratic function is shown on the graph.
an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
The vertex of the parabola is at (0,0) and the parabola opens upward, so the minimum value of the function occurs at the vertex and is 0. The y-value then increases as we move away from the vertex. The parabola reaches a y-value of 9 at x=3, but the dot is an open circle, which indicates that the function value is not defined at that point. Therefore, the range of the function is:
{y | 0 ≤ y < 9}, since the function value can be any number between 0 (inclusive) and 9 (exclusive). The answer is (c).
Is the following relation a function?
{(3, 2), (3, −2), (1, −4), (−1, 2)}
No, the relation is not a function, since input value x=3 is associated with two different output values y=2 and y=-2. A function has only one output value for each input value.
A study was done by an online retail store to determine the rate at which users used its website. A graph of the data that was collected is shown:
A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn.
What can be interpreted from the range of this graph?
a. The range represents the 54-month time period of the study.
b. The range represents the 36-month time period of the study.
c. The range represents the number of users each month for 36 months.
d. The range represents the number of users each month for 54 months.