Let f(x)= (2/3)^x
Complete each statement.

A. The domain of f(x) is__.

B. The range of f(x) is_.

C. The y-intercept of the graph of f(x) is____.

D. The horizontal asymptote of the graph of f(x) is the ( x-axis / y-axis ). (Circle one.)

E. The graph of f(x) is ( increasing / decreasing ) from left to right. (Circle one.)

F. The value of the ( base / coefficient / exponent ) determines whether the graph of an exponential
function is increasing or decreasing from left to right. (Circle one.)

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isyllus isyllus · Answer 1 · 2020-07-24T03:32:37+02:00

Answer:

A. All real number

B. Positive Real numbers

C. y intercept is 1

D. x axis

E. Decreasing

F. Base

Step-by-step explanation:

Given:

[tex]f(x) = (\frac{2}{3})^x[/tex]

A.

Domain of a function f(x) is the value of 'x' for which it has a defined value.

Here, f(x) can have any real number to be given to x.

So, domain is all real numbers.

B.

Range of a function f(x) is the value of f(x) when we give some value of x as input.

Here, we can not have negative value of f(x) because x is in the exponent.

So, the range is Positive Real numbers.

C.

y intercept of any function f(x) is the value of f(0).

[tex]f(0)=(\frac{2}{3})^0 = 1[/tex]

So, y intercept is 1.

D. Horizontal asymptote is the the line where value of [tex]x \rightarrow \infty[/tex]

x axis is the answer.

E. The graph is decreasing with increasing value of x(from left to right).

Because the base is less than 1.

F. The value of base determines whether the graph will be decreasing or increasing.

If base > 1, the graph will be increasing will increasing value of exponent (x).

Here the base is less than 1 so decreasing graph.

Please refer to the attached graph for better understanding of the given function.