Question

just started on this unit help please:)
For what values of b is f(x) = bx a decreasing function???

Answer 1

A. Any real number
B. b > 0
C. b > 1
D. 0 < b < 1

Answer 2

b could be gradient
negative is decreasing...im not sure...

Answer 3

think about it this way

b > 0

y = 5x x = 3, y = 15
y = 6x x = 4, y = 24
y = 7x x = 5, y = 35
...

now

b < 0

y = -5x x = 3, y = -15
y = -6x x = 4, y = -24
y= -7x x = 5, y = -35
...

off those 2 lines, which one do you think is showing a "decreasing function graph"?

Answer 4

I would say b<0 is decreasing

Answer 5

but that isn't one of the choices:/

Answer 6

confusion

Answer 7

now let's check if 0 < b < 1

y = 5/10x x = 3, y = 15/10
y = 6/10x x = 4, y = 24/10
y = 7/10x x = 5, y = 35/10
...

y = -5/10x x = 3, y = -15/10
y = -6/10x x = 4, y = -24/10
y = -7/10x x = 5, y = -35/10
...

Answer 8

so the function will seem to stick in the I and IV Quadrants only
on the 1st quadrant is "ascending"
on the 4th quadrant is "descending"

Answer 9

... actually, my negative fractions are less than 0 :/

Answer 10

Hmm ya your options don't seem to make sense....

Was the function in question suppose to be, \(\large f(x)=b^x\)

Answer 11

lemme retry that one

Answer 12

now let's check if 0 < b < 1

y = 5/10x x = 3, y = 15/10
y = 6/10x x = 4, y = 24/10
y = 7/10x x = 5, y = 35/10
...

is always in the 1st quadrant, and always ascending for that scenario

Answer 13

pauli is it an exponential function as zepdrix pointed out?