Question 1012078
in all of these, the domain is all real values of x


the range and the y-intercept for each is shown below:


a) y=2(4)^x


the range is all real value of y > 0.
the y-intercept is y = 2 * 4^0 = 2*1 = 2.
the function is increasing form left to right.
that's the red equation in the graph shown below.


b) y=3(1/2)^x


the range is all real values of y > 0.
the y-intercept is y = 3 * (1/2)^0 = 3 * 1 = 3.
the function is decreasing from left to right.
that's the blue equation in the graph shown below.


c) y=-(0.3)^x


the range is all real values of y < 0.
the y-intercept is equal to -(0.3)^0 = -1.
the graph is increasing from left to right.
that's the green equation in the graph shown below.


d) y=-3(5.2)^x


the range is all real values of y < 0.
the y-intercept is equal to -3 * (5.2)^0 = -3 * 1 = -3.
the graph is decreasing from left to right.
that's the purple equation in the graph shown below:


see below the graph for further comments.


<img src = "http://theo.x10hosting.com/2016/010301.jpg" alt="$$$" </>


2*4^x is increasing because, as x gets larger, 4^x gets larger.


3*(1/2)^x is decreasing because, as x gets larger, (1/2)^x gets smaller.


(1/2)^1 = 1/2
(1/2)^2 = 1/4
etc.


-.3^x is increasing because, as x gets larger, .3^x gets smaller and so minus .3^x gets larger.


.3^1 = .3
.3^2 = .09
.09 is smaller than .3


-.3^1 = -.3
-.3^2 = -.09
-.09 is larger than -.3


-3*5.2^x is decreasing because, as x gets larger, 5.2^x gets larger and so minus 5.2^x gets smaller.


5.2^1 = 5.2
5.2^2 = 27.04
27.04 is larger than 5.2


-5.2^1 = -5.2
-5.2^2 = -27.04
-27.04 is smaller than -5.2