A function in which the y-values form a geometric sequence is referred to as a geometric function. In such functions, each successive value is obtained by multiplying the previous value by a constant ratio. This characteristic means that for a given input, the output values follow a specific pattern defined by the geometric sequence.
The term that describes a function in which the values follow an arithmetic sequence is called a "linear function." In this context, a linear function can be expressed in the form ( f(x) = mx + b ), where ( m ) represents the constant difference between successive values, and ( b ) is the initial value. The graph of a linear function is a straight line, reflecting the constant rate of change characteristic of arithmetic sequences.
y = a*r^n where a and r are non-zero constants, and n is a counter.
Domain describes all possible input values.
The range of the function.
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A function in which the y-values form a geometric sequence is referred to as a geometric function. In such functions, each successive value is obtained by multiplying the previous value by a constant ratio. This characteristic means that for a given input, the output values follow a specific pattern defined by the geometric sequence.
linear function
The term that describes a function in which the values follow an arithmetic sequence is called a "linear function." In this context, a linear function can be expressed in the form ( f(x) = mx + b ), where ( m ) represents the constant difference between successive values, and ( b ) is the initial value. The graph of a linear function is a straight line, reflecting the constant rate of change characteristic of arithmetic sequences.
y = a*r^n where a and r are non-zero constants, and n is a counter.
Domain describes all possible input values.
The range of the function.
To find the fifth term of the geometric sequence 8, 0, 4, 0, 20, we need to identify a pattern. The terms appear to alternate between zero and other values, but there might be a misunderstanding since the terms provided don't follow a consistent geometric ratio. Assuming the sequence is correct as given, the fifth term is 20.
The range of a function is the set of all possible input values.
A sequence can be both arithmetic and geometric if it consists of constant values. For example, the sequence where every term is the same number (e.g., 2, 2, 2, 2) is arithmetic because the difference between consecutive terms is zero, and it is geometric because the ratio of consecutive terms is also one. In such cases, the sequence meets the criteria for both types, as both the common difference and the common ratio are consistent.
domain
Domain