Choose all that represent an exponential function.
a. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 14 | 10 | 6 | 2 | -2 | -6 | -10
b. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 1/2 | 1 | 2 | 4 | 8 | 16 | 32
c. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | -14 | -9 | -4 | 1 | 6 | 11 | 16
d. x | -3 | -2 | -1 | 0 | 1 | 2 | 3
y | 4 | 8 | 16 | 32 | 64 | 128 | 256
I am sorry they are not lined up! I tried my best and I believe the answers are C and D. Can someone check for me?
I'm sorry, but your best wasn't good enough this time. It seems you made a mistake - the correct answers are B and D. Exponential functions have a constant ratio between the y-values for every increase in x by a constant amount, and option B exhibits this pattern with each y-value doubling. Meanwhile, option D also shows an exponential relationship, with each y-value being multiplied by 2.
Yes, you are correct. The exponential functions are represented by Options C and D.
In Option C, the values of y are increasing or decreasing by a common ratio each time x increases by 1. For example, when x increases from -1 to 0, y increases from -4 to 1, which is a common ratio of 5. This is a characteristic of exponential functions.
In Option D, the values of y are also increasing or decreasing by a common ratio each time x increases by 1. For example, when x increases from 0 to 1, y increases from 32 to 64, which is a common ratio of 2. Again, this is a characteristic of exponential functions.
Options A and B do not represent exponential functions because the values of y are not increasing or decreasing by a common ratio.
To determine if a function is exponential, you need to check if the y-values are increasing or decreasing at a constant rate as the x-values increase or decrease.
Let's analyze each option:
a. The y-values are decreasing by a constant rate of 4 as the x-values increase by 1. This is not an exponential function.
b. The y-values are increasing by a constant rate of multiplying by 2 as the x-values increase by 1. This is an exponential function.
c. The y-values are increasing by a constant rate of 5 as the x-values increase by 1. This is not an exponential function.
d. The y-values are increasing by a constant rate of multiplying by 2 as the x-values increase by 1. This is an exponential function.
So, in this case, the exponential functions are options B and D.