Which facts are true for the graph of the function below? Check all that apply.𝐹(𝑥)=(35)𝑥F(x)=( 53 ) x A.It is increasing.B.The domain of F(x) is x > 0.C.It is decreasing.D.The range of F(x) is y > 0.E.The x-intercept is (1, 0).F.The y-intercept is (0, 1).SUBMITarrow_backPREVIOUS
Question
Which facts are true for the graph of the function below? Check all that apply.𝐹(𝑥)=(35)𝑥F(x)=( 53 ) x A.It is increasing.B.The domain of F(x) is x > 0.C.It is decreasing.D.The range of F(x) is y > 0.E.The x-intercept is (1, 0).F.The y-intercept is (0, 1).SUBMITarrow_backPREVIOUS
Solution
The function F(x) = (35)^x is an exponential function. Here are the facts that apply to this function:
A. It is increasing. This is true because for exponential functions with a base greater than 1, as x increases, F(x) also increases.
B. The domain of F(x) is x > 0. This is not true. The domain of an exponential function is all real numbers, which means x can be any number, not just greater than 0.
C. It is decreasing. This is not true. As mentioned in point A, the function is increasing, not decreasing.
D. The range of F(x) is y > 0. This is true. The range of an exponential function with a positive base is always (0, ∞), which means y is always greater than 0.
E. The x-intercept is (1, 0). This is not true. The x-intercept of an exponential function is the value of x for which F(x) = 0. For this function, there is no real number x that will make F(x) = 0.
F. The y-intercept is (0, 1). This is true. The y-intercept of an exponential function is the value of F(x) when x = 0. For this function, F(0) = (35)^0 = 1, so the y-intercept is (0, 1).
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