Question

Select all the correct answers. function g is a transformation of the parent exponential function. which statements are true about function g? a) the range of function g is (3,infinity) function g is 4 units above f. b) the domain of function g is x>0. c) function g is positive over the interval (-infinity,infinity). d) function g decreasing over the interval (-infinity,0) function g has a y-intercept of (0,4)

Answer 1

The range of function g is (3, infinity), function g is positive over the interval (-infinity, infinity), and function g is decreasing over the interval (-infinity, 0).

Step-by-step explanation:

The correct statements about function g, a transformation of the parent exponential function, are:

a) The range of function g is (3, infinity). This means that the output values of function g are greater than 3. For example, g(4) = 8 is a valid output.

c) Function g is positive over the interval (-infinity, infinity). This means that all the output values of function g are positive. For example, g(2) = 6 is positive.

d) Function g is decreasing over the interval (-infinity, 0). This means that as the input values decrease from negative infinity to zero, the corresponding output values of function g decrease. For example, g(-1) = 9 is greater than g(-2) = 7.

Answer 2

The correct statements about function g as a transformation of the parent exponential function are likely a) and c), as these align with the properties of exponential functions.

Step-by-step explanation:

To determine which statements are true about function g being a transformation of the parent exponential function, we need to understand the properties of exponential functions and transformations. From the given options:

Option a) might be true if function g is a vertical shift of the parent function, as the normal range of an exponential function is (0, infinity).

Option b) is incorrect because the domain of any exponential function is all real numbers, not just x>0.

Option c) can be true since exponential functions are always positive for any real number input.

Option d) is incorrect assuming the exponential function has a positive base because exponential functions are increasing over the interval (-infinity, infinity), including (-infinity, 0).

Thus, the correct statements about function g as a transformation of a parent exponential function would be a) and c).