Exponential Functions Concepts Assessment

The video tutorial explains exponential functions, focusing on exponential decay and growth. It describes how the graph behaves based on the value of 'a', whether it is between 0 and 1 or greater than 1. The domain of these functions is all real numbers, and the range is from 0 to infinity. The graph features a horizontal asymptote at y=0 and a y-intercept at 1. Key points for graphing include (0,1), (1,a), and (-1,1/a).

What happens to the graph of an exponential function when the base 'a' is between 0 and 1?

• The graph remains constant.

• The graph decreases as x increases.

• The graph increases as x increases.

• The graph oscillates.

What is the term used to describe the behavior of an exponential function when the base is greater than 1?

• Logarithmic growth

• Exponential growth

• Linear growth

• Exponential decay

What is the domain of all exponential functions?

• All positive numbers

• All negative numbers

• All real numbers

• All integers

What is the range of an exponential function that has not been transformed?

• All numbers greater than zero

• All positive numbers

• All real numbers

• All numbers less than zero

Where is the horizontal asymptote of an exponential function located?

• At y = 1

• At x = 0

• At x = 1

• At y = 0

What is the y-intercept of an exponential function?

• a^0

• a

• 1

• 0

Which point is always included in the graph of an exponential function?

• (1,0)

• (0,1)

• (1,1)

• (0,0)

What is the value of the function at x = 1 for an exponential function with base 'a'?

• 0

• 1/a

• 1

• a

What is the value of the function at x = -1 for an exponential function with base 'a'?

• 1

• a

• 1/a

• 0

Which of the following is NOT a key point of a parent exponential function?

• (0,1)

• (1,a)

• (-1,1/a)

• (a,0)