The slope of a linear function is also a measure of how fast the function is increasing or decreasing. The only difference is that the slope of a straight line remains the same throughout the domain of the line.
If the rate of change is a measure of how fast the function is increasing, the slope will be positive. If the rate of change is a measure of the function decreasing, the slope will be negative.
no... the sign indicates whether the rate of change is increasing or decreasing. It is only negative if the rate is decreasing over time.
To increase something means to make it bigger, and to decrease something means to make it smaller. These are used often with numerical values (numbers), e.g. I increased (made bigger) 20 to 30. Here I am increasing by 10, etc.
if a function is increasing, the average change of rate between any two points must be positive.
6
"The base of the exponent" doesn't make sense; base and exponent are two different parts of an exponential function. To be an exponential function, the variable must be in the exponent. Assuming the base is positive:* If the base is greater than 1, the function increases. * If the base is 1, you have a constant function. * If the base is less than 1, the function decreases.
no... the sign indicates whether the rate of change is increasing or decreasing. It is only negative if the rate is decreasing over time.
No.
solid heat
The rate of change of velocity, either increasing or decreasing, is its acceleration or deceleration.
Increasing speed, decreasing speed, and change of direction
higher pressure will compress the particules and lower pressure will separate them
To increase something means to make it bigger, and to decrease something means to make it smaller. These are used often with numerical values (numbers), e.g. I increased (made bigger) 20 to 30. Here I am increasing by 10, etc.
if a function is increasing, the average change of rate between any two points must be positive.
The rate of change of air pressure as a function of increasing altitude decreases with increasing altitude.
No. Acceleration IS a change of velocity - any change. When velocity increases, there IS acceleration. The acceleration itself may be increasing, decreasing, or remain constant.
breaking or creating molecular bonds -- increasing or decreasing heat energy
You can change both of these by increasing or decreasing the speed of the molecules (kinetic energy), or by increasing or decreasing the heat applied (thermal energy). If you want to melt ice, you can increase the kinetic energy by increasing the thermal energy. The opposite occurs if you want to freeze water.