Which statements are true of the function f(x) = 3(2.5)x? Check all that apply.The function is exponential.
The initial value of the function is 2.5.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers.
The range of the function is all real numbers greater than 3.
Answers
The statements which are true of the function; f(x) = 3(2.5)^x and there explanations are below;
- The function is exponential;Traditional to every exponential function is that the independent variable is usually an exponent of a constant. Hence, we can conclude the function is an exponential function.
- Yes,the function increases by a factor of 2.5 for each unit increase in x. Hence, the slope of the function is; 2.5.
- The domainof the function is all real number, because, the value of y is defined for all real number values of x.
Read more on exponential functions;
This is an exponential function since the x is in the exponent's place instead of in the place of a "regular" variable. The first statement is true.
The initial value of this particular function is 3 (the other number is the multiplier), so choice 2 is NOT true.
The function increases by its multiplier, which is 2.5, so statement 3 is true.
The equation allows us to enter any x value we want to determine the y, so the domain is in fact all real numbers. So, this statement is also true.
If you were to graph this on a calculator, you would see that the range, the "allowed" y values for our function, do not touch or ever drop below the x-axis. That means that the range is all numbers greater than 0. So that statement is false. No matter what value we pick for x, we will NEVER get back a negative y value or that y = 0. For example, if x = 0, y = 3; if x = -5, y = .03; if x = -10, y = .0003; if x = 5, y = 292.97; if x = -100, . Y will never be equal to 0 or less than 0.
Related Questions
Solve the following system by any method. 2x – 6y = 24 –5x + 6y = –6 A. (4, –1) B. (0, –6) C. (6, –1) D. (–6, –6)
What is the discriminant of the given equation ?X^2-2x+2+0 a)-12 b)8 c)-4 d)-8
Can someone help? This is sooooo hard!!
Consider the following system of equations: y = −2x + 3 y = x − 5 Which description best describes the solution to the system of equations? Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis. Line y = −2x + 3 intersects line y = x − 5. Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis. Line y = −2x + 3 intersects the origin.
What is
21 times x = 7
Answers
Answer:
x = 1/3
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other:
21x = 7
Divide 21 from both sides:
(21x)/21 = (7)/21
x = 7/21
x = 1/3
x = 1/3 is your answer.
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Answer: is 3 unless you mean that the x=7 if you mean that then it would be 147
A. personal
B. business
C. government
Answers
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of an economy as a whole rather than individual markets.
Answer:
C. government
Step-by-step explanation:
Answers
6x-6=9x+18
6x=9x+24
-3x=24
-x=8
x=-8
Answers
Answer:
9=48
Step-by-step explanation:
shown above in the photo hope it helps
Answer:
9) x = 32
11) x = 33.3
Step-by-step explanation:
9) 1/4x = 8
4 x 1/4x = 8 x 4
X = 32
11) 3/5x = 20
5 x 3/5x = 20 x 5
3x = 100
3x ÷ 3 = 100 ÷ 3
X = 33.33333
X = 33.3
Answers
For the given function, f(x) = 2x^6 - 2x^2 - 5, as x becomes extremely large in either the positive or negative direction, the function value grows without bound, heading towards positive infinity. This behavior is a characteristic of functions with even degrees and positive leading coefficients.
Analyzing the end behavior of a function is a valuable tool in understanding how the function behaves as the input, denoted by 'x', approaches positive or negative infinity. In this case, we are given the function f(x) = 2x^6 - 2x^2 - 5 and tasked with determining its end behavior.
Degree of the Function: The degree of a function is the highest power of the variable it contains. In our function, the highest power of the variable 'x' is 6, as it appears in the term 2x^6.
Leading Coefficient: The leading coefficient is the coefficient of the term with the highest power. In our function, the leading coefficient is 2, associated with the term 2x^6.
With these pieces of information, we can deduce the end behavior of the function:
The degree of the function is 6, which is an even degree.
The leading coefficient is 2, and it's positive.
For a function with an even degree and a positive leading coefficient, the end behavior is as follows:
As x approaches positive infinity (+∞), the function value f(x) also approaches positive infinity (+∞).
As x approaches negative infinity (-∞), the function value f(x) also approaches positive infinity (+∞).
For more such information on: function
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What is the standard deviation of the data set?
Round to the nearest tenth.
Question 5.5. What is the standard deviation of the data set? Round your answer to the nearest tenth.
6 4 9 5 5 4 5
(Points : 1)
1.6
1.7
5.4
5.0
Answers
Answer:
Step-by-step explanation:
(A) It is given that a data set has a variance of 42, then the standard deviation is given as:
⇒
⇒
Thus, the standard deviation of the given data set is 6.48.
(B) The given data set is:
6 4 9 5 5 4 5
Mean of the given data set is:
Data set
6 0.33
4 2.01
9 12.81
5 0.17
5 0.17
4 2.01
5 0.17
The variance is given as:
Thus, the standard deviation is given as:
⇒
⇒
Hence, option A is correct.
Q5.5
To find the standard variation first find the mean of the set.
6+4+9+5+5+4+5 = 38
Then we will subtract the mean from each number in the set, then will square that. Then we will add those all.
Solution is in the pic. Sorry if this was not explanatory enough.
Ask me if you wanna know more.