is this function - y=3^x open up or down? is it a vertical stretch or compression?
I answered this on Friday. See the related questions below.
Was there something unclear?
yes, about the vertical compression and strecth
and how the range is y>0
if x>0, 3^x > 1
if x<0, 3^x is between 0 and 1.
There is no value of x that will produce a negative result.
As for the stretch, I have to ask again, compared to what?
3^x is stretched when compared to 2^x, but it is compressed when compared to 4^x.
Hmmm. ACtually, on the stretch, I'd gave to say neither.
a^x passes through (0,1) for any value of a. So there can be no vertical scale factor. The stretch/compression is reversed as you cross the y-axis.
i don't understand. its fine
To determine if the function y=3^x opens up or down and if it undergoes a vertical stretch or compression, let's analyze the properties of the function.
In this equation, the base of the exponential function is 3. Therefore, we need to remember two key facts about exponential functions:
1. If the base of the exponential function is greater than 1 (in this case, 3), the function will open upward. This is because as x increases, the value of 3^x will also increase.
2. There is no vertical stretch or compression in exponential functions. The term "vertical stretch" or "compression" is used in relation to functions like linear or quadratic, where we multiply the entire function by a value greater than 1 or between 0 and 1, respectively. However, in an exponential function, we do not multiply by a constant to achieve a vertical stretch or compression.
So, to answer your question:
- The function y=3^x opens upward because the base (3) is greater than 1.
- There is neither a vertical stretch nor compression in exponential functions.
In summary, the function y=3^x opens up and does not have a vertical stretch or compression.