Which of the following is a decreasing function?

Question

a. y = 7^x - 2
b. y = 7^-x + 2
c. y = 3(5^x) - 5
d. y = 5(3^x) + 3

What function is the reflection of y = 10^x with respect to the y-axis?
a. y = -10^x
b. y = (-1/10)^x
c. y = 10^-x
d. y = -10^x

Answer 1

#1, the key terms in each answer is the power term
pick any two increasing values of x
e.g.
x = 2, y = 7^2 - 2 = 47
x = 3 , y = 7^3 - 2 = 341
Is there any reason for this pattern NOT to continue,
so the function is INCREASING
You will see the same for c) and d)
Now look at b)
x=2 , y = 7^-2 - 2 = 1/49 - 2 = appr - 7.97959..
x=3 , y = 1/343 - 2 = appr -1.997..
which is LOWER or smaller than the y value at x=2
So the function would be decreasing.

2. for a reflection in the y-xis
any point (a,b) ---> (-a,b)

so a point on y = 10^2 is (2,100)
so its reflection in the y-axis would be (-2,100)

can you decide which equation would be satisfied by the point (-2,100) ?