(04.02 LC)
Two functions, function A and function B, are shown below:
Function A
x y
7 14
8 16
9 18
Function B
The first quadrant of a coordinate grid is shown from 0 to positive 10 on both axes at intervals of 1. The title is Function B. Only the even numbers are shown on the scale. A line is drawn by connecting the points on ordered pairs 2, 4 and 3, 6 and 4, 8.
Which statement best compares the rate of change of the two functions? (1 point)
The rate of change of both functions is 2.
The rate of change of both functions is 3.
The rate of change of function A is greater than the rate of change of function B.
The rate of change of function B is greater than the rate of change of function A.
The correct answer is: The rate of change of function A is greater than the rate of change of function B.
A standard showerhead in Marty's house dispenses 7 gallons of water per minute. Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead.
y = 3x
How much water does Marty save each day with the change in showerheads if he uses the shower for 8 minutes each day? (1 point)
4 gallons
12 gallons
32 gallons
53 gallons
To find out how much water Marty saves each day, we need to calculate the difference between the amount of water dispensed by the standard showerhead and the amount dispensed by the new energy-saving showerhead for 8 minutes.
For the standard showerhead, 7 gallons of water are dispensed per minute. So, for 8 minutes, it would dispense 7 * 8 = 56 gallons of water.
For the new energy-saving showerhead, the amount of water dispensed is given by the equation y = 3x. So, if Marty uses the shower for 8 minutes, the amount of water dispensed would be 3 * 8 = 24 gallons.
Therefore, the amount of water Marty saves each day with the change in showerheads is 56 - 24 = 32 gallons.
Therefore, Marty saves 32 gallons of water each day.
Which of the following is a linear function? (1 point)
y = 3x2
y = 1 over 3x
y = x3 + 5
2 over 3x = y − 1
The linear function among the given options is: y = 1 over 3x.
The graph shows a journey in a car. Which of the statements most likely describes the journey at the portion of the graph labeled K? (1 point)
A line graph is drawn on the first quadrant of a coordinate plane. The x-axis is labeled Time in seconds, and the y-axis is labeled Distance in miles. The line graph is divided into 7 segments labeled I, J, K, L, M, N, and O. I starts at the origin and is a straight line slanting up. J is a line segment that starts at the end of I and is horizontal. K is a curve that starts at the end of J and curves up. L is a straight line that starts at the end of K and is horizontal. M is a straight line that starts at the end of L and slopes down. N is a straight line that starts at the end of M and is horizontal. O is a curve that starts at the end of N and curves down to finally touch the x-axis.
The car travels the same distance per unit of time because the portion shows a linear, increasing function.
The car travels different distances per unit of time because the portion shows a linear, increasing function.
The car travels different distances per unit of time because the portion shows a nonlinear, increasing function.
The car travels the same distance per unit of time because the portion shows a nonlinear, increasing function.