Step-by-step explanation
Let us see the graph of the given function.
Now, let us see the different answer choices.
Option A. The range of F(x) is y > 4.
The range of a function is the set of its possible output values. In other words, it is the resulting y-values we get after substituting all the possible x-values.
As we can see in the graph, the range of the function is all real numbers greater than zero. Thus, the range of F(x) is y > 0. Therefore, the statement is false.
Option B. The y-intercept is (0,3) and option F. The y-intercept is (0,4).
The y-intercept is the point where the graph crosses the y-axis. In this case, we have:
Therefore, statement B is true, and statement F is false.
Option C. It is decreasing, and option E. It is increasing.
• A function decreases when the y-value decreases as the x-value increases.
,
• A function increases when the y-value increases as the x-value increases.
In this case, we have:
As we can see, the F(x) graph is increasing, not decreasing.
D. The domain of F(x) is all real numbers.
The domain of a function is the set of all values for which the function is defined. In the case of exponential functions, the domain is all real numbers, as we see in the F(x) graph. Therefore, the statement is true.
Answer
The facts that are true for the graph of F(x) are:
B. The y-intercept is (0,3)
D. The domain of F(x) is all real numbers.
E. It is increasing.