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Consider the function y = an
If a < -1 it oscillates between negative and positive values, with the oscillations increasing.
If a = -1, it oscillates between -1 and 1.
If -1 < a < 0 it oscillates between negative and positive values, with the oscillations deceasing.
if 0 < a < 1, it is decreasing.
If a = 1, it is 1 for all n
If a > 1, it is increasing.
What else can I help you with?
How can you tell from a linear equation which direction it goes without graphing the equation?
You must find the slope, if it is positive, then the line is always increasing. If it is negative, then the line is always decreasing.
How do you tell if ordered pairs satisfy an exponential function?
To determine if ordered pairs satisfy an exponential function, you can check if they follow the form (y = ab^x), where (a) is a constant, (b) is the base (a positive number), and (x) is the independent variable. For each pair ((x, y)), calculate (b) by rearranging the equation as (b = \frac{y}{a}) for a given (x) and (y). If the ratio of (y) values corresponding to successive (x) values remains constant, the pairs likely satisfy an exponential function. Additionally, plotting the points should show a characteristic exponential curve.
How do you tell if its exponential growth or decay?
Exponential growth has a growth/decay factor (or percentage decimal) greater than 1. Decay has a decay factor less than 1.
What does the horizontal line tell you about a function?
If the function is a one-to-one function, therefore it has an inverse.
How can you tell by looking at a graph if the represntation is a function?
if a certain abscissa corresponds to more than one ordinate, then it is not a function.
How can you tell whether the gradient of a curve is increasing or decreasing?
Differentiate the curve twice and then enter a value for x. If the answer is positive, the gradient is increasing at that point. If the answer is negative, the gradient is decreasing at that point. And if the answer is zero, the gradient is not changing.
What does the slope tell you about a function?
If you want to find the initial value of an exponential, which point would you find on the graph?
How can you tell from looking at an elation if the equation represents experiential growth or decay?
To determine if an equation represents exponential growth or decay, look at the base of the exponential function. If the base is greater than 1 (e.g., (y = a \cdot b^x) with (b > 1)), the function represents exponential growth. Conversely, if the base is between 0 and 1 (e.g., (y = a \cdot b^x) with (0 < b < 1)), the function indicates exponential decay. Additionally, the sign of the exponent can also provide insight into the behavior of the function.
What do the turning points of the graph tell you?
The turning points of a graph indicate where the function changes direction, signaling local maxima and minima. Specifically, a turning point corresponds to a change in the sign of the first derivative, which means the function is either increasing or decreasing before and after that point. Analyzing these points helps identify critical features of the function, such as the overall shape and behavior, which can be useful for optimization and understanding trends.
How can you tell from a linear equation which direction it goes without graphing the equation?
You must find the slope, if it is positive, then the line is always increasing. If it is negative, then the line is always decreasing.
How do you tell if ordered pairs satisfy an exponential function?
To determine if ordered pairs satisfy an exponential function, you can check if they follow the form (y = ab^x), where (a) is a constant, (b) is the base (a positive number), and (x) is the independent variable. For each pair ((x, y)), calculate (b) by rearranging the equation as (b = \frac{y}{a}) for a given (x) and (y). If the ratio of (y) values corresponding to successive (x) values remains constant, the pairs likely satisfy an exponential function. Additionally, plotting the points should show a characteristic exponential curve.
How can you tell if a graph could be an exponential decay function?
it slopes downward. it has a negative slope. it it really high when it is close to zero but gets really low as the x-value goes greater.
How do you know if the moon is increasing or decreasing in the amount of light?
You can tell if the moon is increasing or decreasing in light by observing its shape in the sky. During a waxing moon, it will appear to be growing larger, while during a waning moon, it will appear to be shrinking. Additionally, a waxing moon will be visible in the evening, while a waning moon will be visible in the morning.
How to tell the difference of a linear and non linear function without it on a graph?
A linear function, of a variable x, is of the form ax+b where a and b are constants. A non-linear function will have x appearing in some other form: raised to a power other than 1, or in a trigonometric, or exponential or other form.
How can you tell on a distance time graph if the object is moving towards or away from you?
Only if you know your location (the coordinate on the distance scale and the time scale) where "you" are can you infer if the object is moving towards you (the absolute distance to the object is decreasing) or away from you (the distance is increasing).
How do you tell if its exponential growth or decay?
Exponential growth has a growth/decay factor (or percentage decimal) greater than 1. Decay has a decay factor less than 1.
How can you tell if an exponential function is exponential growth or decay by looking at its base?
It is not enough to look at the base. This is because a^x is the same as (1/a)^-x : the key is therefore a combination of the base and the sign of the exponent.0 < base < 1, exponent < 0 : growth0 < base < 1, exponent > 0 : decaybase > 1, exponent < 0 : decaybase > 1, exponent > 0 : growth.
