Question

identify the key features for the function (y = 5^x). select all that apply.

range: (y > 0)
(b = 5)
range: ((-infty, +infty))
(a = 1)
domain: ((-infty, +infty))
(a = 5)
domain: (y > 0)
(b = 1)

Explanation:

Identify parameters \(a\) and \(b\)

The exponential function is in the standard form \(y = a \cdot b^x\).
For \(y = 5^x\):

$$ a = 1, \quad b = 5 $$

Determine the domain

An exponential function of the form \(y = 5^x\) is defined for all real numbers.

$$ \text{Domain: } (-\infty, +\infty) $$

Determine the range

Since the base \(b = 5 > 0\) and the coefficient \(a = 1 > 0\), the function values are always strictly positive.

$$ \text{Range: } y > 0 $$

Answer:

• Range: \(y > 0\) (Correct answer)
• \(b = 5\) (Correct answer)
• Range: \((-\infty, +\infty)\)
• \(a = 1\) (Correct answer)
• Domain: \((-\infty, +\infty)\) (Correct answer)
• \(a = 5\)
• Domain: \(y > 0\)
• \(b = 1\)