You have two exponential functions. One function has the formula g(x) = 3 x . The other function has the formula h(x) = 2-x . Wh
ich option below shows the graph of k(x) = (g - h)(x)?
1 answer:
Answer:
see graph
Step-by-step explanation:
g(x) = 3^ x .
h(x) = 2^-x
We want to subtract them
f(x) = 3^x - 2^(-x)
I will rewrite without the negative exponent
f(x) = 3^x - (1/2)^(x)
Lets pick a couple of points
f(0) = 3^0 - (1/2) ^ 0 = 1-1 = 0
As x gets large 3^x gets large and 1/2^x gets close to 0, so it will get large
As x goes to negative infinity, 3^x goes to zero and 1/2^ gets large so we get - infinitity
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Answer and Step-by-step explanation:
1) If you graph the lines, you will get the lines in the first attachment. You will see that the intersection point is (3, 5), which is the solution to that system.
2) First, let's convert both of these into slope-intercept form so that they're easier to graph.
x - 3y = 2
x = 3y + 2
3y = x - 2
y =
AND
-3x + 9y = -6
9y = 3x - 6
y =
We see that these two lines are exactly the same, which means that no matter what coordinate works for one, it will work for the other. In other words, there are infinitely many solutions.
And, if you graph these lines, you will get the graph in the second attachment, where they are the same line.
Hope this helps!
