Exponential Function Properties and Analysis

The video tutorial explores the function f(x) = 12 * 1.45^x, highlighting its characteristics as an increasing exponential function. It explains the domain and range, emphasizing that the domain includes all real numbers and the range consists of positive numbers. The tutorial also covers graphical analysis, noting that the graph does not cross the x-axis, and discusses the horizontal asymptote at y=0.

What is the function we are considering in this lesson?

• f(x) = 10 * 1.5^x

• f(x) = 12 * 1.45^x

• f(x) = 12 * 1.4^x

• f(x) = 15 * 1.4^x

Why is the function f(x) = 12 * 1.45^x considered increasing?

• Because the base is negative

• Because the base is equal to 1

• Because the base is less than 1

• Because the base is greater than 1

What is the base of the function f(x) = 12 * 1.45^x?

• 12

• 0

• 1.45

• x

What is the significance of the base being greater than one in f(x) = 12 * 1.45^x?

• It makes the function undefined

• It makes the function constant

• It makes the function increasing

• It makes the function decreasing

What is the initial value of the function f(x) = 12 * 1.45^x?

• 12

• 0

• 1

• 1.45

What happens to the function f(x) = 12 * 1.45^x when x is zero?

• The function equals 1.45

• The function equals zero

• The function equals x

• The function equals 12

How is the domain of the function f(x) = 12 * 1.45^x represented?

• Only integers

• All real numbers

• Only positive numbers

• Only negative numbers

Which notation can be used to represent the domain of f(x) = 12 * 1.45^x?

• Set notation

• Graphical notation

• Inequality notation

• Matrix notation

What is the range of the function f(x) = 12 * 1.45^x?

• Greater than zero

• Equal to zero

• All real numbers

• Less than zero

Why are the outputs of f(x) = 12 * 1.45^x always positive?

• Because the base is less than one

• Because the base is zero

• Because the base is negative

• Because the base is greater than one