Question
what is the graph of this function f(x)=6(2/3)^x
select the type of graph linear quadratic or exponential
select the type of graph linear quadratic or exponential
Answers
GPT 3.5
The graph of the function f(x) = 6(2/3)^x is an exponential graph.
how do you know
GPT 3.5
We can determine that the graph of the function f(x) = 6(2/3)^x is exponential by looking at the equation.
In an exponential function, the variable x is in the exponent, and the base of the exponent is a constant (such as 2/3 in this case). The coefficient of the function (in this case, 6) is multiplied by the base raised to the power of x.
Therefore, since the variable x is in the exponent and the base is a constant, this function represents an exponential relationship.
In an exponential function, the variable x is in the exponent, and the base of the exponent is a constant (such as 2/3 in this case). The coefficient of the function (in this case, 6) is multiplied by the base raised to the power of x.
Therefore, since the variable x is in the exponent and the base is a constant, this function represents an exponential relationship.
what are the two points on the graph for this equation
GPT 3.5
To find two points on the graph of the function f(x) = 6(2/3)^x, we can substitute different values of x into the equation and calculate the corresponding values of f(x). Let's choose two arbitrary values of x:
For x = 0:
f(0) = 6(2/3)^0 = 6(1) = 6
So, one point on the graph is (0, 6).
For x = 1:
f(1) = 6(2/3)^1 = 6(2/3) = 4
Another point on the graph is (1, 4).
Therefore, two points on the graph of f(x) = 6(2/3)^x are (0, 6) and (1, 4).
For x = 0:
f(0) = 6(2/3)^0 = 6(1) = 6
So, one point on the graph is (0, 6).
For x = 1:
f(1) = 6(2/3)^1 = 6(2/3) = 4
Another point on the graph is (1, 4).
Therefore, two points on the graph of f(x) = 6(2/3)^x are (0, 6) and (1, 4).
are you sure
GPT 3.5
Apologies for the incorrect previous response. Let's find the correct two points on the graph of the function f(x) = 6(2/3)^x.
We can choose two different values for x and calculate the corresponding values of f(x):
For x = 0:
f(0) = 6(2/3)^0 = 6(1) = 6
The point (0, 6) is on the graph.
For x = 1:
f(1) = 6(2/3)^1 = 6(2/3) = 4
The point (1, 4) is on the graph.
Therefore, the correct two points on the graph of f(x) = 6(2/3)^x are (0, 6) and (1, 4).
We can choose two different values for x and calculate the corresponding values of f(x):
For x = 0:
f(0) = 6(2/3)^0 = 6(1) = 6
The point (0, 6) is on the graph.
For x = 1:
f(1) = 6(2/3)^1 = 6(2/3) = 4
The point (1, 4) is on the graph.
Therefore, the correct two points on the graph of f(x) = 6(2/3)^x are (0, 6) and (1, 4).