Exponential Functions Concepts and Graphs

The video tutorial covers exponential functions, focusing on transformations, reflections, shifts, and compressions or stretches. It explains the parent exponential function f(x) = a^x, where the base 'a' determines the graph's shape. If 'a' is greater than 1, the function is increasing, forming a ramp or swoop shape. Key points for graphing include (-1, 1/a), (0, 1), and (1, a). The domain is all real numbers, and the range is from 0 to infinity, with a horizontal asymptote at y = 0. The video also discusses functions where 'a' is between 0 and 1, resulting in a decreasing ramp shape. The key points, domain, range, and asymptote remain consistent, with the main difference being the direction of the graph's growth.

What transformations can be applied to exponential functions?

• Scaling, rotation, and translation

• Translation, rotation, and reflection

• Reflection, shifting, compression, and stretching

• Reflection, rotation, and scaling

What is the general form of the parent exponential function?

• f(x) = x/a

• f(x) = a^x

• f(x) = x^a

• f(x) = a*x

If the base 'a' of an exponential function is greater than 1, what is the shape of the graph?

• Vertical line

• Increasing ramp

• Horizontal line

• Decreasing ramp

What are the key points used for sketching the graph of an exponential function with a base greater than 1?

• (-1, 0), (0, a), (1, 1)

• (-1, 1), (0, a), (1, 0)

• (-1, a), (0, 0), (1, 1/a)

• (-1, 1/a), (0, 1), (1, a)

What is the domain of an exponential function?

• 0 to 1

• 0 to infinity

• Negative infinity to infinity

• Negative infinity to 0

What is the horizontal asymptote of an exponential function?

• y = 1

• x = 1

• y = 0

• x = 0

What is the range of an exponential function?

• 1 to infinity

• Negative infinity to 0

• 0 to infinity

• Negative infinity to infinity

If the base 'a' of an exponential function is between 0 and 1, what is the shape of the graph?

• Vertical line

• Decreasing ramp

• Horizontal line

• Increasing ramp

What are the key points used for sketching the graph of an exponential function with a base between 0 and 1?

• (-1, 1/a), (0, 1), (1, a)

• (-1, a), (0, 0), (1, 1/a)

• (-1, 2), (0, 1), (1, 1/2)

• (-1, 1), (0, a), (1, 0)

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

• It becomes a horizontal line

• It becomes a vertical line

• It becomes an increasing ramp

• It becomes a decreasing ramp