Exponential Functions and Their Properties

The video tutorial explores an exponential function f(x) = 3 * 12^x, focusing on finding the Y-intercept, common ratio, and asymptote. It explains that the Y-intercept is the value of the function when x is zero, which is 3 in this case. The common ratio is identified as 1/2, and the asymptote is discussed as the value the function approaches as x becomes very large, which is y = 0. An example problem is presented to find a function with a Y-intercept of 4.5.

What is the initial value of the exponential function f(x) = 3 * 12^x?

• 3

• 12

• 0

• 1

How do you find the Y-intercept of an exponential function?

• Find the common ratio

• Find the slope of the function

• Evaluate the function at x = 0

• Evaluate the function at x = 1

What is the Y-intercept of the function f(x) = 3 * 12^x?

• 3

• 12

• 1

• 0

In an exponential function, what does the common ratio represent?

• The Y-intercept

• The slope of the function

• The initial value

• The base of the exponent

What is the common ratio of the function f(x) = 3 * 12^x?

• 3

• 1

• 1/2

• 12

As x approaches positive infinity, what value does the function f(x) = 3 * 12^x approach?

• Twelve

• Three

• Zero

• Infinity

What is the asymptote of the function f(x) = 3 * 12^x as x becomes very large?

• y = Infinity

• y = 0

• y = 12

• y = 3

Which of the following functions has a Y-intercept of 4.5?

• j(x) = 2 * 3^x

• h(x) = 3 * 4.5^x

• g(x) = 4.5 * 2^x

• f(x) = -1 * 2^x

How do you determine if a function has a Y-intercept of 4.5?

• Check if the common ratio is 4.5

• Check if the slope is 4.5

• Check if f(1) = 4.5

• Check if f(0) = 4.5

What is the Y-intercept of the function h(x) = 3 * 4.5^x?

• 0

• 3

• 1

• 4.5