EXPONENTIAL FUNCTIONS TASK

Question

i) Create an exponential function, m(x), that contains the point (5,3). Verify, using any technique that m(x) contains the point (5,3). Then, design an equivalent exponential function to m(x), using a different base. Verify, using any technique that they are in fact equivalent.

ii) Your function, m(x), undergoes a reflection (either vertical or horizontal - you choose) and a vertical translation of 5 units . Graph this new function AND m(x) by hand. What is the y-intercept of this new function, y=n(x)? Justify your answer. What is the new range of this function? Justify.

Answer 1

f(x) = ab^x + c

f(3) = 5 = ab^3 + c

let a=1, c=0

5 = b^3

b = cube root of 5 = about 1.71

f(1.71) =1.71 ^3 = about 5.0002

for another base, change a or c or both

f(x) =ab^x + c, let a=1 and c= 5

then

f(x) = b^x + 5

5 = b^x + 5

b^x = 0

x = cube root of 0 = 0

b= 0

f(x) = ab^x + c

f(x) = 1(0)^x +

f(x) = 5

or

f(x) = 5b^x with a=5 and c= 0

f(3) = 5 = 5b^x

b^3 = 5/5 = 1

b = cube root of 1 = 1

f(x) =5(1)^x

f(3) = 5(1)^3 = 5