Video Transcript
What is the amplitude of the
function 𝑓 𝑥 is equal to 𝑎 sin of 𝑏 multiplied by 𝑥 minus ℎ plus 𝑘?
Well, the first thing we want to do
is actually, if we have a function in this form, is to identify what each part
means. Well, we start on the right-hand
side. And we’ve got plus 𝑘. Well, the plus 𝑘 is actually the
vertical shift of our function. Moving along to the left, the ℎ is
actually the horizontal shift. And 𝑏 actually helps us to
determine the period. And it does this because we have a
formula. And that formula is that the period
is equal to two 𝜋 over the absolute value of 𝑏. And so that’s how we use 𝑏 to find
the period. We get that two 𝜋 because two 𝜋
is actually the period of the function sin 𝑥.
Okay, great. So we’ve got those three parts of
this function determined. Now let’s look at the last part,
𝑎. Well, we look at 𝑎. So 𝑎 is actually the amplitude of
our function. Okay, great. So now we actually know what each
part tells us. To solve the problem, it says what
is the amplitude of our function? Well, we get to the point. We could say that therefore, the
amplitude of the function 𝑎 sin of 𝑏 multiplied by 𝑥 minus ℎ plus 𝑘 is going to
be 𝑎.
