Look at the relation in the graph. Which choice best represents the domain?
−2,0,1,5 −2,3,4,5 0,1,4,5 −3,0,4,5
Based on the graph, the possible x-values (domain) are -2, 0, 1, and 5. Therefore, the choice that best represents the domain is −2,0,1,5.
The table represents some points on the graph of a linear function.
Which function represents this relationship?
y = − 32 x + 4 y = − 32 x − 1 4 y = − 23 x − 9 y = − 23 x − 1
Graph
X. Y.
-2. -11
2. -17
4. -20
To find the function that represents the given points, we can choose any pair of points and use the point-slope form to write the equation. Let's choose the points (-2, -11) and (2, -17).
Using the point-slope form, the equation is:
y - y1 = m(x - x1)
For the point (-2, -11):
y - (-11) = m(x - (-2))
y + 11 = m(x + 2)
For the point (2, -17):
-17 + 11 = m(2 + 2)
-6 = 4m
m = -6/4
m = -3/2
Substituting the value of m into the equation, we have:
y + 11 = -3/2(x + 2)
Simplifying the equation:
2y + 22 = -3(x + 2)
2y + 22 = -3x - 6
2y = -3x - 6 - 22
2y = -3x - 28
y = (-3/2)x - 14
Therefore, the function that represents the given relationship is y = (-3/2)x - 14.
A construction worker built steps up to a home. The table shows the linear relationship between the height off the ground in inches and the number of steps.
What is the rate of change of height off the ground with respect to the number of steps?
8 in. per step
16 in. per step
1/8 in. per step
1/16 in.per Step
Graph
Number of steps.
3
5
7
9
11
Height
20
36
52
68
84
To find the rate of change of the height off the ground with respect to the number of steps, we need to determine the change in height divided by the change in the number of steps.
Let's consider the first two points: (3, 20) and (5, 36).
Change in height = 36 - 20 = 16 inches
Change in number of steps = 5 - 3 = 2 steps
Rate of change = Change in height / Change in number of steps = 16 / 2 = 8 inches per step.
Therefore, the rate of change of height off the ground with respect to the number of steps is 8 inches per step.