Use the following graph to estimate the rate of change of the function at x=0.6
using the points (0,0)
and (1,−0.5)
(1 point)
Responses
The rate of change is -2
The rate of change is -2
The rate of change is -0.5
The rate of change is -0.5
The rate of change is -3
The rate of change is -3
The rate of change is -1
The rate of change at x=0.6 can be estimated by finding the slope of the line passing through the points (0,0) and (1,-0.5).
The slope of a line can be calculated using the formula: slope = (y2 - y1)/(x2 - x1).
Plugging in the values from the given points, we have:
slope = (-0.5 - 0) / (1 - 0) = -0.5 / 1 = -0.5
Therefore, the rate of change at x=0.6 is -0.5.
the following graph to estimate the rate of change of the function at x=0.5
using the points (−1, −1)
and (1,3)
(1 point)
Responses
The rate of change is -0.5
The rate of change is -0.5
The rate of change is 2
The rate of change is 2
The rate of change is 0.5
The rate of change is 0.5
The rate of change is -2
The rate of change at x=0.5 can be estimated by finding the slope of the line passing through the points (-1,-1) and (1,3).
The slope of a line can be calculated using the formula: slope = (y2 - y1)/(x2 - x1).
Plugging in the values from the given points, we have:
slope = (3 - (-1)) / (1 - (-1)) = (3 + 1) / (1 + 1) = 4 / 2 = 2
Therefore, the rate of change at x=0.5 is 2.
The following graph shows the inches of snow on the ground over a certain number of hours. Use the graph to estimate the rate of change of the function at 3 hours using the points (0,0)
and (5, 10)
(1 point)
Responses
The rate of change is 2 inches per hour
The rate of change is 2 inches per hour
The rate of change is -0.5 of an inch per hour
The rate of change is -0.5 of an inch per hour
The rate of change is 0.5 of an inch per hour
The rate of change is 0.5 of an inch per hour
The rate of change is -2 inches per hour
The rate of change at 3 hours can be estimated by finding the slope of the line passing through the points (0,0) and (5,10).
The slope of a line can be calculated using the formula: slope = (y2 - y1)/(x2 - x1).
Plugging in the values from the given points, we have:
slope = (10 - 0) / (5 - 0) = 10 / 5 = 2
Therefore, the rate of change at 3 hours is 2 inches per hour.
The following graph shows the average temperatures in degrees Fahrenheit over the days of month. Use the graph to estimate the rate of change of the function at the ninth day of the month using the points (2,55)
and (10,65)
(1 point)
Responses
The rate of change is 1.25 degrees Fahrenheit per day.
The rate of change is 1.25 degrees Fahrenheit per day.
The rate of change is -0.8 degrees Fahrenheit per day.
The rate of change is -0.8 degrees Fahrenheit per day.
The rate of change is -1.25 degrees Fahrenheit per day.
The rate of change is -1.25 degrees Fahrenheit per day.
The rate of change is 0.8 degrees Fahrenheit per day.
The rate of change is 0.8 degrees Fahrenheit per day.
The rate of change at the ninth day can be estimated by finding the slope of the line passing through the points (2, 55) and (10, 65).
The slope of a line can be calculated using the formula: slope = (y2 - y1)/(x2 - x1).
Plugging in the values from the given points, we have:
slope = (65 - 55) / (10 - 2) = 10 / 8 = 1.25
Therefore, the rate of change at the ninth day of the month is 1.25 degrees Fahrenheit per day.
Use the graph below to complete the sentence indicating which points would provide the most accurate estimate for the rate of change of the function as it crosses the y-axis.
(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Response area and Response area would provide the most accurate estimation. The slope of the line drawn between these two points appears closest to the slope of the function at x=0
The option "open paren 0 point 5 comma 1 close paren" (4 of 4) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
Based on the given information, the response should be "(-0.5, 1) and (0.5, 1)". These points would provide the most accurate estimation for the rate of change of the function as it crosses the y-axis. The slope of the line drawn between these two points appears closest to the slope of the function at x=0.
Write a recursive formula for the sequence {12, 9, 6, 3...}
.(1 point)
Responses
f(1)=−3
, f(n)=f(n−1)+12
, for n>1
f of 1 is equal to negative 3, f left parenthesis n equals f left parenthesis n minus 1 right parenthesis plus 12 , for n greater than 1
f(1)=12
, f(n)=f(n−1)−3
, for n>1
f left parenthesis 1 right parenthesis equals 12 , f left parenthesis n equals f left parenthesis n minus 1 right parenthesis minus 3 , for n greater than 1
f(1)=3
, f(n)=f(n−1)−12
, for n>1
f of 1 is equal to 3, f left parenthesis n equals f left parenthesis n minus 1 right parenthesis minus 12 , for n greater than 1
f(1)=12
, f(n)=f(n−1)+3
, for n>1