The equation y = a^x is a decreasing function a =
1) 1
2) 2
3) -3
4) .25
I think that the correct answer is 3) -3...but I am not sure why? Can anyone please check if I am right and explain why? Please....Thank you for your help!!!
In y = ax^2 , the parabola opens upwards for a positive value of a
and it opens downwards for a negative value of a
so have confidence in your answer since ...
Thanks for your help!!! :)
To determine whether the equation y = a^x is a decreasing function, we need to analyze how the value of x affects the value of y.
For a function to be decreasing, it means as x increases, y decreases.
Let's substitute different values of x to see how y changes for each option:
1) For a = 1, y = 1^x
- If we substitute different positive values of x, y will still be equal to 1. For example, when x = 2, y = 1^2 = 1.
- This indicates that y remains constant, and the function is not decreasing.
- So, option 1) is incorrect.
2) For a = 2, y = 2^x
- If we substitute positive values of x, y will increase as x increases.
- For example, when x = 1, y = 2^1 = 2, and when x = 2, y = 2^2 = 4.
- This indicates that y increases with increasing x, and the function is not decreasing.
- So, option 2) is incorrect.
4) For a = 0.25, y = (0.25)^x
- If we substitute positive values of x, y will decrease as x increases.
- For example, when x = 1, y = (0.25)^1 = 0.25, and when x = 2, y = (0.25)^2 = 0.0625.
- This indicates that y decreases with increasing x, and the function is decreasing.
- So, option 4) is correct.
Now, let's analyze option 3):
3) For a = -3, y = (-3)^x
- If we substitute different positive values of x, y will alternate between negative and positive values.
- For example, when x = 1, y = (-3)^1 = -3, and when x = 2, y = (-3)^2 = 9.
- This indicates that y does not strictly decrease as x increases; it alternates in sign.
- Since the function is not strictly decreasing, option 3) is incorrect.
Therefore, the correct answer is option 4) 0.25.