Several ordered pairs from a continuous exponential function are shown in the table.
2 answers:
Answer:
The function's domain is all real numbers, represented as {x: x ∈ R}, while the range consists of positive y values, depicted as {y: y > 0}
Step-by-step explanation:
* Let's go through the problem-solving steps
- The standard equation for a continuous exponential function can be expressed as
where 'a' signifies the starting value and 'k' denotes the growth factor
- We have several ordered pairs derived from the continuous exponential
function
- The ordered pairs include:
(0, 4), (1, 5), (2, 6.25), (3, 7.8125)
- We will substitute the x and y values into the equation to determine 'a,'
∵
∵ For the first ordered pair where x = 0 and y = 4
- Insert x and y into the equation
∴
∴
- This results in = 1
∴ Hence, a = 4
- Next, we substitute this value of 'a' back into the equation
∴
∵ In the first ordered pair where x = 1 and y = 5
- Insert these x and y values into the equation
∴
∴
- Now, divide both sides by 4
∴ = 1.25
- Substitute the computed value into the equation
- The domain encompasses all x values that make the function valid
- The range includes y values that correspond to x
∵ The function does not become undefined for any x value
∴
Thus, the domain is all real numbers∵ y is never negative
∴
Consequently, the range is all positive real numbers
*
The function's domain consists of {x: x ∈ R}, while the range consists of {y: y > 0}
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