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.
The y-axis represents the number of users, and the highest value on the y-axis is 60,000 (or 60 in thousands), which means that the maximum number of users in any given month during the study was 60,000. However, the line graph only goes up to a y-value of about 54,000 (or 54 in thousands), which suggests that 54,000 was the highest recorded value during the 36-month study period.
Therefore, the correct interpretation of the range of the graph is (b) The range represents the 36-month time period of the study.
Five-year-old students at an elementary school were given a 30-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x axis and Age of Runner on the y axis. The x axis has a scale from 0 to 80 in increments of 10. The y axis has a scale of 0 to 6 in increments of 2. A straight line connecting 30, 5 and 60, 5 is drawn.
Which statement best describes the domain of the function represented in the graph?
5 ≤ x ≤ 60, or x is from 5 to 60
5 ≤ x ≤ 30, or x is from 5 to 30
30 ≤ x ≤ 60, or x is from 30 to 60
0 ≤ x ≤ 30, or x is from 0 to 30
The x-axis represents the distance in yards, and the line graph shows how far the average student ran in 30 seconds. The graph starts at a distance of 30 yards, which is the head start that the 5-year-old students were given. The graph then goes up to a distance of 60 yards, which seems to be the maximum distance that any of the students ran in 30 seconds.
Therefore, the best description of the domain of the function represented in the graph is (c) 30 ≤ x ≤ 60, or x is from 30 to 60. This is the range of distances that the students ran during the race.
Dylan created color panels for a wall using a mix of only green and blue paints. He plotted the quantities of blue and green paints used for each mix and connected them using a line segment, as shown in the graph.
A line graph titled Color Mix, with Quantity of Blue Paint, in millimeters, on the x axis and Quantity of Green Paint, in millimeters, on the y axis. The x axis has a scale from 0 to 10 with an increment of 1. The y axis has a scale of 0 to 20 in increments of 2. A straight line connecting 1, 2 and 9, 14 is drawn.
Which statement best describes the domain of the function represented in the graph?
0 ≤ x ≤ 9
2 ≤ x ≤ 14
1 ≤ x ≤ 9
1 ≤ x ≤ 14
The x-axis represents the quantity of blue paint used, and the line graph shows the quantity of green paint used for each color mix. The graph starts at a quantity of 1 millimeter of blue paint and goes up to a quantity of 9 millimeters of blue paint.
Therefore, the best description of the domain of the function represented in the graph is (c) 1 ≤ x ≤ 9, which represents the range of quantities of blue paint used in the color mixes.
Iris's Botanical Garden produced flowers throughout the year. A graph demonstrating how many flowers she produced over a 11-month period is shown:
A graph of a curve with x axis labeled Months and y axis labeled Number of Flowers Produced. The x-axis ranges from 0 to 11 in increments of 1 and the y-axis ranges from 0 to 120 in increments of 10. The curve starts at about 1 comma 42 and goes up to 6 comma 120 at the highest point and ends at about 11 comma 42.
What can be interpreted from the domain of this graph?
The domain represents a 180-month period of flower production.
The domain represents a 11-month period of flower production.
The domain represents the total number of flowers produced each month.
The domain represents the total number of flowers produced in 11 months.
The x-axis of the graph represents the time period of 11 months, with the graph showing how many flowers were produced in each month. Therefore, the best interpretation of the domain of the graph is that (b) The domain represents an 11-month period of flower production.
Is the following relation a function? Justify your answer.
Two circles are shown, one labeled x and the other labeled y. The x circle contains the numbers 6, negative 1, and 4. The y circle contains the numbers 2, negative 1, and 3. Arrows map numbers from x to numbers from y. There are arrows going from 6 to 3, from negative 1 to 2, from negative 1 to negative 1, and from 4 to 3.
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value