Question

Which facts are true for the graph of the function below? Check all that apply F(x)= 2•5^x

Answer 1

The graph of this equation is an exponential equation. On the left side of the y-axis it is very small. Then on the right side, it goes up quickly.

The following are all true:

The domain is all numbers.
The y-intercept is (0, 2)
It is increasing.

Answer 2

The correct options are:

• The domain of f(x) is all real numbers.
• The y-intercept is (0,2).
• It is increasing.

Explanation:

We have to find the facts that are true for the graph of the function f(x) which is given as:

`f(x)=2.5^x`

Clearly we could see that the function f(x) is a exponential function with base 5.

A)

The domain of f(x) is all real numbers.

This option is correct.

Since f(x) takes all the real values as it is defined everywhere in the real line.

B)

The range of f(x) is y>5.

This option is incorrect since the range of y is y>0.

C)

The y-intercept is (0,2)

since the y-intercept is a point on the graph where x is 0.

So, from the graph we could clearly observe that when x=0.

y=2.

Hence, option C is correct.

D)

It is decreasing.

This function is false.

As the curve is a increasing curve.

E)

The y-intercept is (0,5).

This option is incorrect.

Since the y-intercept is (0,2).

F)

It is increasing.

This option is true.

since the graph is an increasing curve in the domain.