Question

Which function is shown in the graph below?

Answer 1

Answer: The correct option is 2.

Explanation:

From the given figure it is easily noticed that the graph intersect the y-axis at y=9 , therefore the y-intercept is (0,9).

To find the equation of the curve put x=0 in each option, If we get y=9 then that option is true.

Option 1:

$y=(\frac{1}{2})^{(x+3)}-1$

$y=(\frac{1}{2})^{(0+3)}-1=\frac{1}{8}-1=\frac{-7}{8}$

Option 2:

$y=(\frac{1}{2})^{(x-3)}+1$

$y=(\frac{1}{2})^{(0-3)}+1=8+1=9$

Option 3:

$y=(\frac{1}{2})^{(x-1)}+3$

$y=(\frac{1}{2})^{(0-1)}+3=2+3=5$

Option 4:

$y=(\frac{1}{2})^{(x+1)}-3$

$y=(\frac{1}{2})^{(0+1)}-3=\frac{1}{2}-3=\frac{-5}{2}$

Only the equation in option 2 have the y-intercept (0,9), therefore the correct answer is option second.

Answer 2

It is the second function:
y=(1/2)^(x-3)
When x=0, the exponent is -3.  (1/2)^-3 is 8.
y = 8+1 = 9