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CCSS Math: 8.F.A.2, HSF.IF.C.9

Two functions, f and
g, are described below. Which of these statements
about f and g is true? So they defined
function f as kind of a traditional linear
equation right over here. And this right over here is g. So this right over
here is g of x. And that also looks
like a linear function. We see it's a kind of a
downward sloping line. So let's look at our choices
and see which of these are true. f and g are both increasing, and
f is increasing faster than g. Well, when I look at g--
Well, first of all, g is definitely decreasing. So we already know
that that's false. And f is also decreasing. We see here it has
a negative slope. Every time we move forward
3 in the x direction, we're going to move down 7
in the vertical direction. So neither of these
are increasing so that's definitely not right. f and g are both increasing. Well, that's
definitely not right. So we know that both f
and g are decreasing. So this first choice says
they're both decreasing, and g is decreasing faster than f. So let's see what
the slope on g is. So the slope on g is every time
we move 1 in the x direction, positive 1 in the
x direction, we move down 2 in the y direction. So for g of x, if we were
to write our change in y over our change in x-- which
is our slope-- our change in y over change in x, when we
move one in the x direction, positive 1 in the
x direction, we move down 2 in the y direction. So our change in y over
change in x is negative 2. So g has a slope of negative 2. f has a slope of negative 7/3. Negative 7/3 is the same
thing as negative 2 and 1/3. So f's slope is more negative. So it is decreasing faster. So g is not decreasing faster
than f. f is decreasing faster than g. So this is not right. And then we have this choice--
f and g are both decreasing, and f is decreasing
faster than g. This is right, right over here. We have this last choice-- g is
increasing but f is decreasing. We know that's not true.
g is actually decreasing.