Question

Identifying Characteristics of the Exponential Function y = bx (b > 1)
The domain of an exponential function is . The range of an exponential function is .

On a coordinate plane, the graph of y = 2 Superscript x is shown. The curve approaches the x-axis in quadrant 2 and then increases quickly into quadrant 1.

Answer 1

Answer:

• domain (-∞, ∞)
• range (0, ∞)

Step-by-step explanation:

The domain is the horizontal extent: all real numbers. -∞ < x < ∞.

The range is the vertical extent: all numbers greater than zero. 0 < y < ∞. (The graph never actually touches y=0, but comes arbitrarily close.)

Answer 2

The domain and range of a function are the set of input and output values the function can take

• The domain of an exponential function is $\mathbf{(-\infty,\infty)}$
• The range of an exponential function is $\mathbf{[0,\infty)}$

The function is given as:

$\mathbf{y = 2^x}$

There is no restriction as to the value of x.

So, the domain of the function is: $\mathbf{(-\infty,\infty)}$

The function is an exponential function.

For an exponential function, where a = 1 and b > 1, the least value of the function is 0

So, the range of the function is: $\mathbf{[0,\infty)}$

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