Question

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply. a) the function is exponentioal b)The initial value of the function is 2.5.
c)The function increases by a factor of 2.5 for each unit increase in x.
d)The domain of the function is all real numbers.
e)The range of the function is all real numbers greater than 3.

Answer 1

Answer:

a) The function is exponential

c) The function increases by a factor of 2.5 for each unit increase in x.

d) The domain of the function is all real numbers.

Step-by-step explanation:

Exponential functions are written y = a(b)ˣ.

a) the function is exponential is true.

"a" represents the initial value, or the y-intercept.

"b" represents the rate of increase or decrease.

"x" and "y" represent points on the function.

Since a = 3, the initial value is 3.

b) The initial value of the function is 2.5 is false.

Since b = 2.5, the rate of change is 2.5

c)The function increases by a factor of 2.5 for each unit increase in x is true.

When you graph the function, (see graph below), you can see the information clearly.

The domain means how far the graph will go left to right. The graph will continue left to negative infinity, and will continue to the right to positive infinity. This make the domain all real numbers.

d)The domain of the function is all real numbers is true.

The range is how far up or down the graph will reach. Exponential functions have a horizontal asymptote, which is where the graph gets very close to touching a horizontal line, but never will. The asymptote is on the left of the y-axis. The range is all real numbers greater than 0.

e)The range of the function is all real numbers greater than 3 is false.

"3" is the initial value, but the graph extends behind the y-axis too.