Which of the following could be an example of a function with a domain (-oo,oo) and a range (-oo,2)? Check all that apply.

A. y= -(3)^x+2

B. y= -(3)^x-2

C. y= -(0.25)^x+2

D/ y= -(0.25)^x-2

Look at A

if x = -2, y = -1/9 + 2 never bigger than 2
if x = +2, y = -9 + 2 goes big -

Look at B
if x = -2, y = -1/9 - 2
if x = +2, y = -9 -2 goes big -

Look at C
if x = -2, y = -1/.125+2
if x = 0, y = 2
if x = +2, -.125+2 approaches 2

Look at D also stays close to 2

A is the only one that goes big negative but is never more positive than 2

Oh, okay. You made it very clear, thanks for the help. :)

You are welcome.

To determine which of the given functions could be an example with a domain of (-oo,oo) and a range of (-oo,2), we need to analyze each function individually.

Let's start with option A: y= -(3)^x+2

To find the domain of this function, we need to consider the base of the exponent, which is 3. Any positive base raised to a real power will result in a positive value. Thus, the domain of this function is (-oo,oo).

Now let's consider the range. In this function, we have a negative sign in front of the exponent, which means all the values will be reflected over the x-axis. Since the base is 3, the function will approach zero as the exponent approaches positive infinity, but it will never reach exactly 0. The range will be (-oo, 2) because the function is approaching but never actually reaching 2.

Therefore, option A could be an example of a function with the given domain and range.

Moving on to option B: y= -(3)^x-2

Like before, the domain of this function is (-oo,oo) because the base is positive.

Regarding the range, we again have a negative sign in front of the exponent, indicating reflection over the x-axis. However, this time the function is being subtracted by 2. So, instead of the range being (-oo, 2), it will be (-oo, -2).

Therefore, option B does not represent a function with the given domain and range.

Next is option C: y= -(0.25)^x+2

The domain is still (-oo,oo) because the base is a positive value.

In this case, the base is between 0 and 1, which means it will decrease as the exponent increases. The function has a negative sign in front of it, so it is reflected over the x-axis. As the exponent approaches positive infinity, the function will approach 0 but never reach it. Adding 2 to this result, the range becomes (2, +oo) because it grows infinitely larger than 2.

Therefore, option C does not represent a function with the given domain and range.

Finally, we have option D: y= -(0.25)^x-2

Like before, the domain is (-oo,oo) due to the positive base.

The range is evaluated using the same reasoning as option C. The base, being between 0 and 1, will decrease as the exponent increases. The negative sign in front of it reflects the function over the x-axis. As the exponent approaches positive infinity, the function will approach 0 but never reach it. Subtracting 2, the range will be (-oo, -2) because it will not go beyond -2.

Therefore, option D could be an example of a function with the given domain and range.

In summary, options A and D could be examples of functions with a domain of (-oo,oo) and a range of (-oo,2).