Hello everyone,

I am having a bit of trouble with these exponential equations (see attached) and was wondering if anyone could please step me through how to do them?

Also, do you times the front and the end numbers (outside of the brackets) together? Or do you just leave them?

Thankyou!

Coolmate 👍

You haven't specified what you want me to do for question j.

With that sketch in question a, you should first note that \( f(x)=a^x\) has asymptote \(y=0\). So in your case, \(f(x) =4(3^x) + 1\) has asymptote \(y=1\). (Which can be properly verified - as \(x\to \infty\), it is clear that there is no asymptote. But as \(x\to -\infty\), we have \(4(3^x)+1 \to 0 + 1 = 1\).

Now the \(4\) gets multiplied to the entire exponential term, i.e. the \(3^x\) bit. So it forms some kind of a stretch (dilation) to just the exponential - it doesn't move the asymptote around. As an example, your \(y\)-intercept is now at \(y=4(1)+1 = 5\), instead of at \(y=2\).

In general, graphically showing the extra factor in front isn't exactly possible. Some points need to be plotted (and the graph drawn to scale) for it to have a noticeable impact. But if you try plotting on Desmos/GeoGebra, it will be 100% clear that some kind of stretching is happening.