Question

exponential functions review
list the attributes for the following exponential function
domain:
range:
asymptote:
y - intercept:
growth or decay:

Explanation:

Step1: Determine Domain

The domain of an exponential function is all real numbers since there are no restrictions on the input \( x \). So, Domain: \( (-\infty, \infty) \) or all real numbers.

Step2: Determine Range

Looking at the graph, the function starts from near \( y = 0 \) (but never touches \( y = 0 \)) and goes upwards. So the range is all real numbers greater than \( 0 \), i.e., \( (0, \infty) \).

Step3: Determine Asymptote

The horizontal asymptote is the line that the function approaches but never touches. From the graph, as \( x \to -\infty \), the function approaches \( y = 0 \). So, Asymptote: \( y = 0 \).

Step4: Determine y - intercept

The y - intercept is the point where \( x = 0 \). From the graph, when \( x = 0 \), \( y = 2 \). So, y - intercept: \( (0, 2) \) or just \( 2 \) (the y - value).

Step5: Determine Growth or Decay

Since the function is increasing as \( x \) increases (the graph goes up from left to right), it is an exponential growth function. So, Growth or Decay: Growth.

Answer:

Domain: \( (-\infty, \infty) \)
Range: \( (0, \infty) \)
Asymptote: \( y = 0 \)
y - intercept: \( 2 \)
Growth or Decay: Growth