Which is the graph of g(x) = (two-thirds) Superscript x – 2?

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)

Question

14-09-2022
Mathematics

Answered

Which is the graph of g(x) = (two-thirds) Superscript x – 2?

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)

Answer :

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facundo3141592 facundo3141592 · Answer 1 · 2022-09-16T08:47:54-04:00

the correct option is:

"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"

Which is the graph of the given function?

Here we have the exponential function:

g(x) = (2/3)^x - 2

Now, remember that for any real number different than zero, we have that:

x^0 = 1

So if we evaluate our function in x= 0 we will get:

g(0) = (2/3)^0 - 2 = 1 - 2 = -1

Then the function passes through the point (0, -1)

With this in mind, we conclude that the correct option is:

"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"

If you want to learn more about exponential functions:

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