Table 21: Table for R 01 2 3 R(x) 6 24 96 384 (a) Assuming that R is an exponent
ID: 2912190 • Letter: T
Question
Table 21: Table for R 01 2 3 R(x) 6 24 96 384 (a) Assuming that R is an exponential function, find a function equation for R. (b) Find the average rate of change of R on the interval 0 2. (c) Using the function equation for R, find the average rate of change of R on the interval 1 s5. (d) Using the function equation for R, what is the range of R on the domain of all real mmbers? (e) Using the function equation for R, write a function equation for the inverse, R-1 (f) Let U(x) -R(2)-3. Describe how the graph of U will differ from the graph of R. Then verify your description using Desmos. (g) What is the range of U? (h) Let V(x) In(R(x). Write a function equation for V.Explanation / Answer
a. R(x) = a bx
24 = 6 b
b= 4
R(x) = 6(4)x
b. (R(2) -R(0))/(2-0) = (96-6)/(2-0) =45
c. R(5)=6(4)5=6144
Average rate of change (R(5)-R(1))/(5-1) = (6144-24)/4 =1530
d.y values cant be negative
So range (0,infinity)
e.R(x)= y = 6(4)x
Switching x and y
x=6(4)y
x/6 = 4y
y= log4(x/6)
R-1(x) = log4(x/6)
f. U(x) = R(2x)-3
Because of 2, the graph stretched horizontally and because of -3 , graph shifts to 3 units down.
g. Range (3,infinity)
h. V(x)= ln (R(x)) = ln(6(4)x) = ln (6)+ x ln (4)
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