Question

What function is represented below?
graph begins in the first quadrant and decreases quickly while crossing the ordered pair 2, 1. Then the graph begins to decrease slowly as it approaches the x axis.

f(x) = one fourth to the power of x plus 2
f(x) = one fourth to the power of x + 2
f(x) = one−fourth to the power of x minus 2
f(x) = one fourth to the power of x − 2

Answer 1

Hi there! Do you have any ideas?

Answer 2

You can see this to see how changing the variables shifts an exponential graph
https://www.desmos.com/calculator/eyjysylzwd

Answer 3

@Khalia

Answer 4

i think its either A or B but im really not sure

Answer 5

Try plugging in 0 in place of x and see what you get for A and B

for a)
\(f(x) = (\frac{1}{2} )^{(0+2)}\)
what is that equal to

for b)
\( f(x) = (\frac{1}{2})^0 + 2\)
what is that equal to

Answer 6

The easy way out is to just graph it using a graphing calculator, but if you're in an exam and don't have access to a graphing calculator, it's useful to know how to actually solve it

Answer 7

This is the easy way out
https://www.desmos.com/calculator/ofgldas5wt

Answer 8

Actually a better point to have tested would have been (2, 1)
(which was given in the question stem)

Answer 9

I plotted the diffent functions, and there is only one that passes through the point (2,1)
Plug the values of x= 2 in the functions and see what value of y you get.