Question

Identify the domain and range of each function. Make sure to provide these answers using inequalities.

a. ƒ(x) = 3(2)x
b. ƒ(x) = 7(0.4)x
c. ƒ(x) = -2(0.6)x
d. ƒ(x) = -3(4)x
e. ƒ(x) = 2(22)x

Answer 1

a. Domain: (-∞, ∞)

Range: (0,∞)

b. Domain: (-∞, ∞)

Range: (0,∞)

c. Domain: (-∞, ∞)

Range: (-∞,0)

d. Domain: (-∞, ∞)

Range: (-∞,0)

e. Domain: (-∞, ∞)

Range: (0,∞)

Explanation:

`a. y= 3(2)^x \\b. y= 7(0.4)^x \\c. y = -2(0.6)^x \\d. y = -3(4)^x \\e. y = 2(22)^x`

These equations are all exponential functions. Exponential functions are curves which approach a horizontal asymptote usually at y=0 or the x-axis unless a value has been added to it. If it has, the curve shifts. None of these have that and their y - values remain between 0 and ∞. This is the range, the set of y values.

However, the range of exponentials can change based on the leading coefficient. If it is negative the graph flips upside down and its range goes to -∞. C and D have this. Their range is (-∞, 0)

In exponential functions, the x values are usually not affected and all are included in the function. Their domain is (-∞, ∞). All of these equations have this domain.

a. Domain: (-∞, ∞)

Range: (0,∞)

b. Domain: (-∞, ∞)

Range: (0,∞)

c. Domain: (-∞, ∞)

Range: (-∞,0)

d. Domain: (-∞, ∞)

Range: (-∞,0)

e. Domain: (-∞, ∞)

Range: (0,∞)