Question

Use the function F(X)=34.2⋅3x to answer the following questions.

What is the domain and range of the function?
a) Domain: All real numbers; Range: All real numbers greater than 34.2
b) Domain: All real numbers; Range: All real numbers
c) Domain: All real numbers greater than 34.2; Range: All real numbers
d) Domain: All real numbers greater than 34.2; Range: All real numbers greater than 34.2
2. What is the initial value of the function?
a) 34.2
b) 68.4
c) 102.6
d) 0
3. What would be the rate of change over the interval [2, 4]?
a) 205.2
b) 34.2
c) 102.6
d) 0

Answer 1

The domain of the function F(X) = 34.2·3^x is all real numbers, and the range is all real numbers greater than 0. The initial value of the function is 34.2. The rate of change over the interval [2, 4] would require further calculation to provide a specific value.

Step-by-step explanation:

When considering the function F(X) = 34.2 · 3x, we can determine the following:

1. The domain is all real numbers, since there are no restrictions on the exponent x in this type of function. Thus, x can be any real number.
2. The range of this function is all real numbers greater than 0, not 34.2. This is because 34.2 is a constant multiplier to the exponential function, which grows without bound but never reaches 0; hence the range starts just above 0.
3. The initial value of the function, which is equivalent to F(0), is 34.2. This is the value of the function when x equals 0.
4. To compute the rate of change over the interval [2, 4], one would calculate the difference in the function values at x=4 and x=2, which is F(4) - F(2).

Thus, the correct answers are:

• Domain: All real numbers; Range: All real numbers greater than 0
• Initial value: 34.2
• Rate of change over the interval [2, 4]: This specific value requires calculation, which hasn't been provided in the prompt.