• As x increases, y decreases.
• As x decreases, y decreases.
• As x increases, y approaches 0.
• As X decreases, Y approaches 0.
• The function is a decreasing function.
3)
The graph of an exponential function has a negative y-intercept and a common ratio (r) such that 0<r<1. Which statements below are true? Select all that apply.
(3 points)
As x increases, y decreases.
• As x decreases, y decreases.
• As x increases, y approaches 0.
• As X decreases, Y approaches 0.
• The function is a decreasing function.
• The function is an increasing function.
3 answers
explain
The statements that are true for the given scenario are:
1. As x increases, y decreases: This is true because the common ratio (r) is between 0 and 1, which means that as x increases, the value of the exponential function decreases.
2. As x decreases, y decreases: This is also true for the same reason as above. As x decreases, with a negative y-intercept and a common ratio (r) between 0 and 1, the value of the exponential function decreases.
3. As x increases, y approaches 0: Since the common ratio (r) is between 0 and 1, as x increases, the exponential function approaches 0 but never reaches it, as it is an asymptote.
4. As x decreases, y approaches 0: This is also true for the same reason as above. As x decreases, the exponential function approaches 0 but never reaches it.
5. The function is a decreasing function: This is true because with a negative y-intercept and a common ratio (r) between 0 and 1, the function will continually decrease as x increases.
Therefore, these are the statements that are true for an exponential function with a negative y-intercept and a common ratio (r) such that 0 < r < 1.
1. As x increases, y decreases: This is true because the common ratio (r) is between 0 and 1, which means that as x increases, the value of the exponential function decreases.
2. As x decreases, y decreases: This is also true for the same reason as above. As x decreases, with a negative y-intercept and a common ratio (r) between 0 and 1, the value of the exponential function decreases.
3. As x increases, y approaches 0: Since the common ratio (r) is between 0 and 1, as x increases, the exponential function approaches 0 but never reaches it, as it is an asymptote.
4. As x decreases, y approaches 0: This is also true for the same reason as above. As x decreases, the exponential function approaches 0 but never reaches it.
5. The function is a decreasing function: This is true because with a negative y-intercept and a common ratio (r) between 0 and 1, the function will continually decrease as x increases.
Therefore, these are the statements that are true for an exponential function with a negative y-intercept and a common ratio (r) such that 0 < r < 1.