Question

Which of these statements is true for f(x) = (1/2)^x

A. The domain of f(x) is x>0.
B. The range of f(x) is y>1/2
C. It is always increasing.
D. The y-intercept is (0,1).

Answer 1

D. The y-intercept is (0,1).

Explanation:

Hope this helps

Answer 2

Answer: D) The y intercept is (0,1)

This can be confirmed by plugging x = 0 into the function to find that...

y = (1/2)^x

y = (1/2)^0

y = 1

Recall that any nonzero value to the 0th power leads to 1. So we can say x^0 = 1 as long as x is not zero.

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Extra info (optional section):

• We can rule out choice A because negative x values work in the domain. For instance, if x = -1, then it leads to y = (1/2)^x = (1/2)^(-1) = 2. The negative exponent will apply the reciprocal operation to the base fraction.
• Choice B can also be ruled out because the range is y > 0. Or you could note that it is possible to get positive y values smaller than 1/2. Try x = 2 and you'll see it leads to y = 1/4 which is not greater than 1/2.
• Choice C is false as well. The function f(x) = (1/2)^x is decreasing throughout the domain. A graph visually would show this due to it going downhill when moving from left to right. A table of values is a non-visual way to see we have a decreasing function. The table would show that y decreases when x increases.