1105 RP2 083 – Evaluating a Composition of Functions from Graphs
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1105 RP2 083 – Evaluating a Composition of Functions from Graphs

September 25, 2019


– [Instructor] Using
the accompanying graphs, find a, g of f of two. To get started, we’ll evaluate f of two. For that, we’ll need
to use the graph of f. First of all, we locate
two along the x axis. We see that a vertical
line intersects the graph at the point two, zero. Therefore, the corresponding
function value is zero. So we’re gonna substitute
zero for f of two. Now we evaluate g of zero. We’ll need to use the graph of g of x. And the zero, which was an output for f, will become an input for g. A vertical line at x is
equal to zero intersects the graph of g at the point zero, one. Therefore, g of zero is equal to one. It follows that g of f
of two is equal to one. For part b, we’re asked to
find f of g of negative one. So first of all, we’ll
evaluate g of negative one using the graph of g. When x is equal to negative one, we see that the corresponding
function value of g is two. So we substitute two
for g of negative one. Now we use the graph
of f to find f of two. F of two is equal to zero, therefore, f of g of negative
one is equal to zero. For part c, we’re to find g of f of zero. So first of all, let’s use the graph of f to evaluate f of zero. From the graph of f, we see that f of zero is equal to four, so we
substitute four for f of zero. We then use the graph of
g to evaluate g of four. The graph of g contains the
point four, negative three, so negative three is equal to g of four. Therefore, g of f of zero
is equal to negative three. Finally, for part d, we’re
asked to find g of f of one. So first of all, we evaluate
f of one using the graph of f. We see that f of one is equal to three, so next, we evaluate g of three. G of three is equal to negative two, so g of f of one is equal to negative two.

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